diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 2cc92c78ac8..8006b60034c 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -42,6 +42,9 @@ New Features
 
 Bug fixes
 ~~~~~~~~~
+- Fix :py:meth:`Dataset.interp` when indexing array shares coordinates with the
+  indexed variable (:issue:`3252`).
+  By `David Huard <https://github.com/huard>`_.
 
 - Fix :py:meth:`Dataset.swap_dims` and :py:meth:`DataArray.swap_dims` producing
   index with name reflecting the previous dimension name instead of the new one
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 7252dd2f3df..4bc18ef78de 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2571,6 +2571,17 @@ def interp(
         coords = either_dict_or_kwargs(coords, coords_kwargs, "interp")
         indexers = dict(self._validate_interp_indexers(coords))
 
+        if coords:
+            # This avoids broadcasting over coordinates that are both in
+            # the original array AND in the indexing array. It essentially
+            # forces interpolation along the shared coordinates.
+            sdims = (
+                set(self.dims)
+                .intersection(*[set(nx.dims) for nx in indexers.values()])
+                .difference(coords.keys())
+            )
+            indexers.update({d: self.variables[d] for d in sdims})
+
         obj = self if assume_sorted else self.sortby([k for k in coords])
 
         def maybe_variable(obj, k):
diff --git a/xarray/tests/test_interp.py b/xarray/tests/test_interp.py
index c2bec2166c8..9cc4933f462 100644
--- a/xarray/tests/test_interp.py
+++ b/xarray/tests/test_interp.py
@@ -244,6 +244,36 @@ def test_interpolate_nd(case):
     assert_allclose(actual.transpose("y", "z"), expected)
 
 
+@requires_scipy
+def test_interpolate_nd_nd():
+    """Interpolate nd array with an nd indexer sharing coordinates."""
+    # Create original array
+    a = [0, 2]
+    x = [0, 1, 2]
+    da = xr.DataArray(
+        np.arange(6).reshape(2, 3), dims=("a", "x"), coords={"a": a, "x": x}
+    )
+
+    # Create indexer into `a` with dimensions (y, x)
+    y = [10]
+    c = {"x": x, "y": y}
+    ia = xr.DataArray([[1, 2, 2]], dims=("y", "x"), coords=c)
+    out = da.interp(a=ia)
+    expected = xr.DataArray([[1.5, 4, 5]], dims=("y", "x"), coords=c)
+    xr.testing.assert_allclose(out.drop_vars("a"), expected)
+
+    # If the *shared* indexing coordinates do not match, interp should fail.
+    with pytest.raises(ValueError):
+        c = {"x": [1], "y": y}
+        ia = xr.DataArray([[1]], dims=("y", "x"), coords=c)
+        da.interp(a=ia)
+
+    with pytest.raises(ValueError):
+        c = {"x": [5, 6, 7], "y": y}
+        ia = xr.DataArray([[1]], dims=("y", "x"), coords=c)
+        da.interp(a=ia)
+
+
 @pytest.mark.parametrize("method", ["linear"])
 @pytest.mark.parametrize("case", [0, 1])
 def test_interpolate_scalar(method, case):