diff --git a/clippy_lints/src/matches.rs b/clippy_lints/src/matches.rs
index cf7650d02bf4..fc265c5231bb 100644
--- a/clippy_lints/src/matches.rs
+++ b/clippy_lints/src/matches.rs
@@ -522,7 +522,7 @@ fn check_wild_enum_match(cx: &LateContext<'_, '_>, ex: &Expr, arms: &[Arm]) {
             }
         }
 
-        let suggestion: Vec<String> = missing_variants
+        let mut suggestion: Vec<String> = missing_variants
             .iter()
             .map(|v| {
                 let suffix = match v.ctor_kind {
@@ -543,11 +543,20 @@ fn check_wild_enum_match(cx: &LateContext<'_, '_>, ex: &Expr, arms: &[Arm]) {
             return;
         }
 
+        let mut message = "wildcard match will miss any future added variants";
+
+        if let ty::Adt(def, _) = ty.kind {
+            if def.is_variant_list_non_exhaustive() {
+                message = "match on non-exhaustive enum doesn't explicitly match all known variants";
+                suggestion.push(String::from("_"));
+            }
+        }
+
         span_lint_and_sugg(
             cx,
             WILDCARD_ENUM_MATCH_ARM,
             wildcard_span,
-            "wildcard match will miss any future added variants.",
+            message,
             "try this",
             suggestion.join(" | "),
             Applicability::MachineApplicable,
diff --git a/tests/ui/wildcard_enum_match_arm.fixed b/tests/ui/wildcard_enum_match_arm.fixed
index af67f326f856..1da2833e2605 100644
--- a/tests/ui/wildcard_enum_match_arm.fixed
+++ b/tests/ui/wildcard_enum_match_arm.fixed
@@ -1,7 +1,9 @@
 // run-rustfix
 
 #![deny(clippy::wildcard_enum_match_arm)]
-#![allow(unreachable_code, unused_variables, dead_code)]
+#![allow(unreachable_code, unused_variables, dead_code, clippy::single_match)]
+
+use std::io::ErrorKind;
 
 #[derive(Clone, Copy, Debug, Eq, PartialEq)]
 enum Color {
@@ -62,4 +64,32 @@ fn main() {
         140 => {},
         _ => {},
     };
+    // We need to use an enum not defined in this test because non_exhaustive is ignored for the
+    // purposes of dead code analysis within a crate.
+    let error_kind = ErrorKind::NotFound;
+    match error_kind {
+        ErrorKind::NotFound => {},
+        std::io::ErrorKind::PermissionDenied | std::io::ErrorKind::ConnectionRefused | std::io::ErrorKind::ConnectionReset | std::io::ErrorKind::ConnectionAborted | std::io::ErrorKind::NotConnected | std::io::ErrorKind::AddrInUse | std::io::ErrorKind::AddrNotAvailable | std::io::ErrorKind::BrokenPipe | std::io::ErrorKind::AlreadyExists | std::io::ErrorKind::WouldBlock | std::io::ErrorKind::InvalidInput | std::io::ErrorKind::InvalidData | std::io::ErrorKind::TimedOut | std::io::ErrorKind::WriteZero | std::io::ErrorKind::Interrupted | std::io::ErrorKind::Other | std::io::ErrorKind::UnexpectedEof | _ => {},
+    }
+    match error_kind {
+        ErrorKind::NotFound => {},
+        ErrorKind::PermissionDenied => {},
+        ErrorKind::ConnectionRefused => {},
+        ErrorKind::ConnectionReset => {},
+        ErrorKind::ConnectionAborted => {},
+        ErrorKind::NotConnected => {},
+        ErrorKind::AddrInUse => {},
+        ErrorKind::AddrNotAvailable => {},
+        ErrorKind::BrokenPipe => {},
+        ErrorKind::AlreadyExists => {},
+        ErrorKind::WouldBlock => {},
+        ErrorKind::InvalidInput => {},
+        ErrorKind::InvalidData => {},
+        ErrorKind::TimedOut => {},
+        ErrorKind::WriteZero => {},
+        ErrorKind::Interrupted => {},
+        ErrorKind::Other => {},
+        ErrorKind::UnexpectedEof => {},
+        _ => {},
+    }
 }
diff --git a/tests/ui/wildcard_enum_match_arm.rs b/tests/ui/wildcard_enum_match_arm.rs
index 049596d342e8..c2eb4b308024 100644
--- a/tests/ui/wildcard_enum_match_arm.rs
+++ b/tests/ui/wildcard_enum_match_arm.rs
@@ -1,7 +1,9 @@
 // run-rustfix
 
 #![deny(clippy::wildcard_enum_match_arm)]
-#![allow(unreachable_code, unused_variables, dead_code)]
+#![allow(unreachable_code, unused_variables, dead_code, clippy::single_match)]
+
+use std::io::ErrorKind;
 
 #[derive(Clone, Copy, Debug, Eq, PartialEq)]
 enum Color {
@@ -62,4 +64,32 @@ fn main() {
         140 => {},
         _ => {},
     };
+    // We need to use an enum not defined in this test because non_exhaustive is ignored for the
+    // purposes of dead code analysis within a crate.
+    let error_kind = ErrorKind::NotFound;
+    match error_kind {
+        ErrorKind::NotFound => {},
+        _ => {},
+    }
+    match error_kind {
+        ErrorKind::NotFound => {},
+        ErrorKind::PermissionDenied => {},
+        ErrorKind::ConnectionRefused => {},
+        ErrorKind::ConnectionReset => {},
+        ErrorKind::ConnectionAborted => {},
+        ErrorKind::NotConnected => {},
+        ErrorKind::AddrInUse => {},
+        ErrorKind::AddrNotAvailable => {},
+        ErrorKind::BrokenPipe => {},
+        ErrorKind::AlreadyExists => {},
+        ErrorKind::WouldBlock => {},
+        ErrorKind::InvalidInput => {},
+        ErrorKind::InvalidData => {},
+        ErrorKind::TimedOut => {},
+        ErrorKind::WriteZero => {},
+        ErrorKind::Interrupted => {},
+        ErrorKind::Other => {},
+        ErrorKind::UnexpectedEof => {},
+        _ => {},
+    }
 }
diff --git a/tests/ui/wildcard_enum_match_arm.stderr b/tests/ui/wildcard_enum_match_arm.stderr
index df90bad15ce1..735f610b7e5d 100644
--- a/tests/ui/wildcard_enum_match_arm.stderr
+++ b/tests/ui/wildcard_enum_match_arm.stderr
@@ -1,5 +1,5 @@
-error: wildcard match will miss any future added variants.
-  --> $DIR/wildcard_enum_match_arm.rs:29:9
+error: wildcard match will miss any future added variants
+  --> $DIR/wildcard_enum_match_arm.rs:31:9
    |
 LL |         _ => eprintln!("Not red"),
    |         ^ help: try this: `Color::Green | Color::Blue | Color::Rgb(..) | Color::Cyan`
@@ -10,23 +10,29 @@ note: lint level defined here
 LL | #![deny(clippy::wildcard_enum_match_arm)]
    |         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-error: wildcard match will miss any future added variants.
-  --> $DIR/wildcard_enum_match_arm.rs:33:9
+error: wildcard match will miss any future added variants
+  --> $DIR/wildcard_enum_match_arm.rs:35:9
    |
 LL |         _not_red => eprintln!("Not red"),
    |         ^^^^^^^^ help: try this: `_not_red @ Color::Green | _not_red @ Color::Blue | _not_red @ Color::Rgb(..) | _not_red @ Color::Cyan`
 
-error: wildcard match will miss any future added variants.
-  --> $DIR/wildcard_enum_match_arm.rs:37:9
+error: wildcard match will miss any future added variants
+  --> $DIR/wildcard_enum_match_arm.rs:39:9
    |
 LL |         not_red => format!("{:?}", not_red),
    |         ^^^^^^^ help: try this: `not_red @ Color::Green | not_red @ Color::Blue | not_red @ Color::Rgb(..) | not_red @ Color::Cyan`
 
-error: wildcard match will miss any future added variants.
-  --> $DIR/wildcard_enum_match_arm.rs:53:9
+error: wildcard match will miss any future added variants
+  --> $DIR/wildcard_enum_match_arm.rs:55:9
    |
 LL |         _ => "No red",
    |         ^ help: try this: `Color::Red | Color::Green | Color::Blue | Color::Rgb(..) | Color::Cyan`
 
-error: aborting due to 4 previous errors
+error: match on non-exhaustive enum doesn't explicitly match all known variants
+  --> $DIR/wildcard_enum_match_arm.rs:72:9
+   |
+LL |         _ => {},
+   |         ^ help: try this: `std::io::ErrorKind::PermissionDenied | std::io::ErrorKind::ConnectionRefused | std::io::ErrorKind::ConnectionReset | std::io::ErrorKind::ConnectionAborted | std::io::ErrorKind::NotConnected | std::io::ErrorKind::AddrInUse | std::io::ErrorKind::AddrNotAvailable | std::io::ErrorKind::BrokenPipe | std::io::ErrorKind::AlreadyExists | std::io::ErrorKind::WouldBlock | std::io::ErrorKind::InvalidInput | std::io::ErrorKind::InvalidData | std::io::ErrorKind::TimedOut | std::io::ErrorKind::WriteZero | std::io::ErrorKind::Interrupted | std::io::ErrorKind::Other | std::io::ErrorKind::UnexpectedEof | _`
+
+error: aborting due to 5 previous errors