diff --git a/dev-requirements.txt b/dev-requirements.txt
index 1abddc7f..3eaf254d 100644
--- a/dev-requirements.txt
+++ b/dev-requirements.txt
@@ -31,7 +31,9 @@ packaging>=21.0; python_version >= '3.6'
 # Virtualenv
 # build requires virtualenv.cli_run which was added in 20.1
 # virtualenv 20.0 requires six<2,>=1.12.0
-virtualenv>=20.1.0
+# virtualenv 20.16.0 removed support for Python<3.6
+virtualenv>=20.15.0; python_version <= '3.11'
+virtualenv>=20.23.0; python_version >= '3.12'
 
 # Coverage reporting (no imports, invoked via coveralls script):
 coverage>=5.0
diff --git a/minimum-constraints.txt b/minimum-constraints.txt
index 001121db..b1c6a91f 100644
--- a/minimum-constraints.txt
+++ b/minimum-constraints.txt
@@ -143,7 +143,8 @@ packaging==20.5; python_version <= '3.5'
 packaging==21.0; python_version >= '3.6'
 
 # Virtualenv
-virtualenv==20.1.0
+virtualenv==20.15.0; python_version <= '3.11'
+virtualenv==20.23.0; python_version >= '3.12'
 
 # Coverage reporting (no imports, invoked via coveralls script):
 coverage==5.0