diff --git a/ci/scripts/integration_dask.sh b/ci/scripts/integration_dask.sh
index eeaba715b6ae7..d1e2ecdc847f2 100755
--- a/ci/scripts/integration_dask.sh
+++ b/ci/scripts/integration_dask.sh
@@ -33,6 +33,9 @@ python -c "import dask.dataframe"
 
 pytest -v --pyargs dask.dataframe.tests.test_dataframe
 pytest -v --pyargs dask.dataframe.io.tests.test_orc
-pytest -v --pyargs dask.dataframe.io.tests.test_parquet
+# skip failing parquet tests
+# test_pandas_timestamp_overflow_pyarrow is skipped because of GH-33321.
+pytest -v --pyargs dask.dataframe.io.tests.test_parquet \
+  -k "not test_pandas_timestamp_overflow_pyarrow"
 # this file contains parquet tests that use S3 filesystem
 pytest -v --pyargs dask.bytes.tests.test_s3