diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index effb199f18e..f0b629fb063 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -29,6 +29,9 @@ Bug Fixes
 - Fix a major performance regression in :py:meth:`Coordinates.to_index` (and
   consequently :py:meth:`Dataset.to_dataframe`) caused by converting the cached
   code ndarrays into Python lists (:issue:`11305`).
+- Fix :py:meth:`DataArray.idxmax` and :py:meth:`DataArray.idxmin` for interval
+  coordinates by preserving pandas extension index adapters during label lookup
+  (:issue:`11300`).
 
 
 Documentation
diff --git a/xarray/compat/array_api_compat.py b/xarray/compat/array_api_compat.py
index e1e5d5c5bdc..52d8506652b 100644
--- a/xarray/compat/array_api_compat.py
+++ b/xarray/compat/array_api_compat.py
@@ -1,5 +1,6 @@
 import numpy as np
 
+from xarray.core.utils import is_allowed_extension_array
 from xarray.namedarray.pycompat import array_type
 
 
@@ -78,5 +79,7 @@ def to_like_array(array, like):
     xp = get_array_namespace(like)
     if xp is not np:
         return xp.asarray(array)
+    if is_allowed_extension_array(array):
+        return np.asarray(array)
     # avoid casting things like pint quantities to numpy arrays
     return array
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 8eb52046a31..d4eaabafc70 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -5530,6 +5530,30 @@ def test_idxmax(
         result7 = ar0.idxmax(fill_value=-1j)
         assert_identical(result7, expected7)
 
+    @pytest.mark.parametrize(
+        ("func_name", "values"),
+        [
+            pytest.param("idxmax", [False, True, True], id="idxmax"),
+            pytest.param("idxmin", [True, False, True], id="idxmin"),
+        ],
+    )
+    def test_idxminmax_interval_coords(
+        self,
+        x: np.ndarray,
+        minindex: int | float,
+        maxindex: int | float,
+        nanindex: int | None,
+        func_name: Literal["idxmax", "idxmin"],
+        values: list[bool],
+    ) -> None:
+        interval_index = pd.IntervalIndex.from_breaks([0, 1, 2, 3])
+        array = xr.DataArray(values, dims=["z"], coords={"z": interval_index})
+
+        result = getattr(array, func_name)()
+
+        expected = xr.DataArray(pd.Interval(1, 2, closed="right"), name="z")
+        assert_identical(result, expected)
+
     @pytest.mark.filterwarnings(
         "ignore:Behaviour of argmin/argmax with neither dim nor :FutureWarning"
     )