diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 6a08246182c..3885b162bd0 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -45,6 +45,9 @@ Bug fixes
   By `Bruce Merry <https://github.com/bmerry>`_.
 - Fix unintended load on datasets when calling :py:meth:`DataArray.plot.scatter` (:pull:`9818`).
   By `Jimmy Westling <https://github.com/illviljan>`_.
+- Fix interpolation when non-numeric coordinate variables are present (:issue:`8099`, :issue:`9839`).
+  By `Deepak Cherian <https://github.com/dcherian>`_.
+
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index ea17a69f827..dd63e52c436 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -4214,10 +4214,11 @@ def _validate_interp_indexer(x, new_x):
                 # interpolated along:
                 variables[name] = var
 
-        if reindex:
-            reindex_indexers = {
+        if reindex and (
+            reindex_indexers := {
                 k: v for k, (_, v) in validated_indexers.items() if v.dims == (k,)
             }
+        ):
             reindexed = alignment.reindex(
                 obj,
                 indexers=reindex_indexers,
diff --git a/xarray/tests/test_interp.py b/xarray/tests/test_interp.py
index d602cb96a6a..e2561515d65 100644
--- a/xarray/tests/test_interp.py
+++ b/xarray/tests/test_interp.py
@@ -1055,3 +1055,23 @@ def test_interp1d_complex_out_of_bounds() -> None:
     expected = da.interp(time=3.5, kwargs=dict(fill_value=np.nan + np.nan * 1j))
     actual = da.interp(time=3.5)
     assert_identical(actual, expected)
+
+
+def test_interp_non_numeric():
+    # regression test for GH8099, GH9839
+    ds = xr.Dataset({"x": ("a", np.arange(4))}, coords={"a": (np.arange(4) - 1.5)})
+
+    t = xr.DataArray(
+        np.random.randn(6).reshape((2, 3)) * 0.5,
+        dims=["r", "s"],
+        coords={"r": np.arange(2) - 0.5, "s": np.arange(3) - 1},
+    )
+
+    ds["m"] = ds.x > 1
+
+    # different dimensions for `x`, compare
+    actual = ds.interp(a=t, method="linear")
+
+    # with numeric only
+    expected = ds[["x"]].interp(a=t, method="linear")
+    assert_identical(actual[["x"]], expected)