diff --git a/package/pyproject.toml b/package/pyproject.toml
index 931cf83aa3a..50f55a3246c 100644
--- a/package/pyproject.toml
+++ b/package/pyproject.toml
@@ -11,4 +11,7 @@ requires = [
     "numpy==1.21.4; python_version=='3.10' and platform_python_implementation != 'PyPy'",
     "setuptools",
     "wheel",
+    # arm64 on Darwin supports Python 3.8 and above and requires numpy>=1.20.0
+    "numpy==1.20.0; python_version=='3.8' and platform_machine=='arm64' and platform_system=='Darwin'",
+    "numpy==1.20.0; python_version=='3.9' and platform_machine=='arm64' and platform_system=='Darwin'",
 ]
diff --git a/testsuite/MDAnalysisTests/analysis/test_encore.py b/testsuite/MDAnalysisTests/analysis/test_encore.py
index 1d5910c04b7..1d6153379e2 100644
--- a/testsuite/MDAnalysisTests/analysis/test_encore.py
+++ b/testsuite/MDAnalysisTests/analysis/test_encore.py
@@ -29,6 +29,7 @@
 import sys
 import os
 import warnings
+import platform
 
 import pytest
 from numpy.testing import assert_equal, assert_almost_equal
@@ -444,6 +445,8 @@ def test_clustering_two_ensembles(self, ens1, ens2):
         assert len(cluster_collection) == expected_value, "Unexpected " \
                                                           "results: {0}".format(cluster_collection)
 
+    @pytest.mark.xfail(platform.machine() == "arm64" and platform.system() == "Darwin",
+                       reason="see gh-3599")
     def test_clustering_three_ensembles_two_identical(self, ens1, ens2):
         cluster_collection = encore.cluster([ens1, ens2, ens1])
         expected_value = 40