diff --git a/python/cudf/cudf/core/index.py b/python/cudf/cudf/core/index.py
index 519b84faea0..8bdf0938dfb 100644
--- a/python/cudf/cudf/core/index.py
+++ b/python/cudf/cudf/core/index.py
@@ -3028,6 +3028,10 @@ def __init__(
         if copy:
             data = column.as_column(data, dtype=dtype).copy()
         kwargs = _setdefault_name(data, name=name)
+
+        if closed is None:
+            closed = "right"
+
         if isinstance(data, IntervalColumn):
             data = data
         elif isinstance(data, pd.Series) and (is_interval_dtype(data.dtype)):
diff --git a/python/cudf/cudf/tests/indexes/test_interval.py b/python/cudf/cudf/tests/indexes/test_interval.py
index 06777c8e6af..f80f6d8bb72 100644
--- a/python/cudf/cudf/tests/indexes/test_interval.py
+++ b/python/cudf/cudf/tests/indexes/test_interval.py
@@ -1 +1,18 @@
 # Copyright (c) 2023, NVIDIA CORPORATION.
+import pandas as pd
+import pyarrow as pa
+
+import cudf
+from cudf.testing._utils import assert_eq
+
+
+def test_interval_constructor_default_closed():
+    idx = cudf.IntervalIndex([pd.Interval(0, 1)])
+    assert idx.closed == "right"
+    assert idx.dtype.closed == "right"
+
+
+def test_interval_to_arrow():
+    expect = pa.Array.from_pandas(pd.IntervalIndex([pd.Interval(0, 1)]))
+    got = cudf.IntervalIndex([pd.Interval(0, 1)]).to_arrow()
+    assert_eq(expect, got)