diff --git a/dev/release/verify-release-candidate.sh b/dev/release/verify-release-candidate.sh
index 61baa219e..2c4c81875 100755
--- a/dev/release/verify-release-candidate.sh
+++ b/dev/release/verify-release-candidate.sh
@@ -354,6 +354,30 @@ test_python() {
   show_info "Testing wheel"
   python -m pytest -vv
 
+  if [ ${TEST_WITH_MEMCHECK} -gt 0 ]; then
+    show_info "Setup environment for Python/valgrind"
+
+    # To have more control over exactly which dependencies are available,
+    # set up a separate venv to run. Essentially, we check for leaks in
+    # all self-contained tests but not tests involving pyarrow or numpy.
+    VALGRIND_PYTHON_VENV="${NANOARROW_TMPDIR}/python/valgrind_venv"
+    python -m venv "${VALGRIND_PYTHON_VENV}"
+    source "${VALGRIND_PYTHON_VENV}/bin/activate"
+    python -m pip install --upgrade pip
+    python -m pip install pytest
+
+    # Ensure we have debug symbols for the build we pass to valgrind
+    export NANOARROW_DEBUG_EXTENSION=1
+    pip install -e .
+
+    show_info "Run Python tests with valgrind"
+    valgrind --tool=memcheck --leak-check=full --error-exitcode=1 \
+        --suppressions="${NANOARROW_SOURCE_DIR}/valgrind.supp" \
+        python -m pytest -vv
+
+    deactivate
+  fi
+
   popd
 }
 
diff --git a/valgrind.supp b/valgrind.supp
index 510778b46..c26db940c 100644
--- a/valgrind.supp
+++ b/valgrind.supp
@@ -28,3 +28,32 @@
     ...
     fun:__tls_get_addr
 }
+
+{
+   <Python>:Handle PyMalloc confusing valgrind (possibly leaked)
+   Memcheck:Leak
+   fun:malloc
+   ...
+   fun:_PyObject_GC_Resize
+}
+
+{
+   <Python>:Handle PyMalloc confusing valgrind (possibly leaked)
+   Memcheck:Leak
+   fun:realloc
+   fun:_PyObject_GC_Resize
+}
+
+{
+   <Python>:Handle PyMalloc confusing valgrind (possibly leaked)
+   Memcheck:Leak
+   fun:malloc
+   fun:_PyObject_GC_New
+}
+
+{
+   <Python>:Handle PyMalloc confusing valgrind (possibly leaked)
+   Memcheck:Leak
+   fun:malloc
+   fun:_PyObject_GC_NewVar
+}