diff --git a/ci/big-endian/Dockerfile b/ci/big-endian/Dockerfile
index 8c70535fc7..b473c47e43 100644
--- a/ci/big-endian/Dockerfile
+++ b/ci/big-endian/Dockerfile
@@ -33,6 +33,10 @@ RUN git clone -q --depth 1 --branch 1.1.2 https://github.com/google/crc32c /tmp/
 RUN python3 -m venv --system-site-packages /venv
 ENV PATH=/venv/bin:$PATH
 RUN pip install -q --no-binary google-crc32c google-crc32c msgspec pytest-accept
+# Debian sid's python3-dateutil 3.0.0 declares a dependency on the `tzdata` distribution,
+# which no Debian package installs, so `pip check` fails on the image as built. tzdata is
+# pure Python; install it from PyPI.
+RUN pip install -q tzdata
 # Debian sid ships numcodecs 0.17.0, which zarr excludes (see pyproject.toml; GHSA-jqc8-qjfv-5m6r),
 # and PyPI has no s390x wheels, so build a satisfying numcodecs from source into the venv, where
 # it shadows the Debian package. Built without isolation so the Debian meson, Cython and numpy