diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index e5eb4680878..ccc779105a0 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -98,6 +98,8 @@ Bug fixes
   :py:meth:`Dataset.to_zarr` (:issue:`4783`, :pull:`4795`).
   By `Julien Seguinot <https://github.com/juseg>`_.
 - Add :py:meth:`Dataset.drop_isel` and :py:meth:`DataArray.drop_isel` (:issue:`4658`, :pull:`4819`). By `Daniel Mesejo <https://github.com/mesejo>`_.
+- Ensure that :py:meth:`Dataset.interp` raises ``ValueError`` when interpolating outside coordinate range and ``bounds_error=True`` (:issue:`4854`, :pull:`4855`).
+  By `Leif Denby <https://github.com/leifdenby>`_.
 - Fix time encoding bug associated with using cftime versions greater than
   1.4.0 with xarray (:issue:`4870`, :pull:`4871`). By `Spencer Clark <https://github.com/spencerkclark>`_.
 
diff --git a/xarray/core/missing.py b/xarray/core/missing.py
index 695affa84c1..e6dd8b537a0 100644
--- a/xarray/core/missing.py
+++ b/xarray/core/missing.py
@@ -154,7 +154,7 @@ def __init__(
             yi,
             kind=self.method,
             fill_value=fill_value,
-            bounds_error=False,
+            bounds_error=bounds_error,
             assume_sorted=assume_sorted,
             copy=copy,
             **self.cons_kwargs,
diff --git a/xarray/tests/test_interp.py b/xarray/tests/test_interp.py
index 20d5fb12a62..cdfc46bbedf 100644
--- a/xarray/tests/test_interp.py
+++ b/xarray/tests/test_interp.py
@@ -866,3 +866,18 @@ def test_interpolate_chunk_advanced(method):
     z = z.chunk(3)
     actual = da.interp(t=0.5, x=x, y=y, z=z, kwargs=kwargs, method=method)
     assert_identical(actual, expected)
+
+
+@requires_scipy
+def test_interp1d_bounds_error():
+    """Ensure exception on bounds error is raised if requested"""
+    da = xr.DataArray(
+        np.sin(0.3 * np.arange(4)),
+        [("time", np.arange(4))],
+    )
+
+    with pytest.raises(ValueError):
+        da.interp(time=3.5, kwargs=dict(bounds_error=True))
+
+    # default is to fill with nans, so this should pass
+    da.interp(time=3.5)