diff --git a/bigframes/pandas/core/methods/describe.py b/bigframes/pandas/core/methods/describe.py
index 6fd7960daf3..34c116ba27d 100644
--- a/bigframes/pandas/core/methods/describe.py
+++ b/bigframes/pandas/core/methods/describe.py
@@ -56,9 +56,10 @@ def describe(
             "max",
         ]
     ).intersection(describe_block.column_labels.get_level_values(-1))
-    describe_block = describe_block.stack(override_labels=stack_cols)
-
-    return dataframe.DataFrame(describe_block).droplevel(level=0)
+    if not stack_cols.empty:
+        describe_block = describe_block.stack(override_labels=stack_cols)
+        return dataframe.DataFrame(describe_block).droplevel(level=0)
+    return dataframe.DataFrame(describe_block)
 
 
 def _describe(
@@ -120,5 +121,7 @@ def _get_aggs_for_dtype(dtype) -> list[aggregations.UnaryAggregateOp]:
         dtypes.TIME_DTYPE,
     ]:
         return [aggregations.count_op, aggregations.nunique_op]
+    elif dtypes.is_json_like(dtype) or dtype == dtypes.OBJ_REF_DTYPE:
+        return [aggregations.count_op]
     else:
         return []
diff --git a/tests/system/small/pandas/test_describe.py b/tests/system/small/pandas/test_describe.py
index 6f288115128..b8e427c10ea 100644
--- a/tests/system/small/pandas/test_describe.py
+++ b/tests/system/small/pandas/test_describe.py
@@ -15,6 +15,8 @@
 import pandas.testing
 import pytest
 
+import bigframes.pandas as bpd
+
 
 def test_df_describe_non_temporal(scalars_dfs):
     # TODO: supply a reason why this isn't compatible with pandas 1.x
@@ -352,3 +354,40 @@ def test_series_groupby_describe(scalars_dfs):
             check_dtype=False,
             check_index_type=False,
         )
+
+
+def test_describe_json_and_obj_ref_returns_count(session):
+    # Test describe() works on JSON and OBJ_REF types (without nunique, which fails)
+    sql = """
+        SELECT
+            PARSE_JSON('{"a": 1}') AS json_col,
+            'gs://cloud-samples-data/vision/ocr/sign.jpg' AS uri_col
+    """
+    df = session.read_gbq(sql)
+
+    df["obj_ref_col"] = df["uri_col"].str.to_blob()
+    df = df.drop(columns=["uri_col"])
+
+    res = df.describe(include="all").to_pandas()
+
+    assert "count" in res.index
+    assert res.loc["count", "json_col"] == 1.0
+    assert res.loc["count", "obj_ref_col"] == 1.0
+
+
+def test_describe_with_unsupported_type_returns_empty_dataframe(session):
+    df = session.read_gbq("SELECT ST_GEOGPOINT(1.0, 2.0) AS geo_col")
+
+    res = df.describe().to_pandas()
+
+    assert len(res.columns) == 0
+    assert len(res.index) == 1
+
+
+def test_describe_empty_dataframe_returns_empty_dataframe(session):
+    df = bpd.DataFrame()
+
+    res = df.describe().to_pandas()
+
+    assert len(res.columns) == 0
+    assert len(res.index) == 1