diff --git a/.evergreen/generated_configs/variants.yml b/.evergreen/generated_configs/variants.yml
index 9bae5f4680..2fe233e087 100644
--- a/.evergreen/generated_configs/variants.yml
+++ b/.evergreen/generated_configs/variants.yml
@@ -167,7 +167,7 @@ buildvariants:
   # Encryption tests
   - name: encryption-rhel8
     tasks:
-      - name: .test-non-standard
+      - name: .test-non-standard !.pypy
       - name: .test-min-deps
     display_name: Encryption RHEL8
     run_on:
@@ -198,7 +198,7 @@ buildvariants:
     tags: [encryption_tag]
   - name: encryption-crypt_shared-rhel8
     tasks:
-      - name: .test-non-standard
+      - name: .test-non-standard !.pypy
       - name: .test-min-deps
     display_name: Encryption crypt_shared RHEL8
     run_on:
@@ -232,7 +232,7 @@ buildvariants:
     tags: [encryption_tag]
   - name: encryption-pyopenssl-rhel8
     tasks:
-      - name: .test-non-standard
+      - name: .test-non-standard !.pypy
     display_name: Encryption PyOpenSSL RHEL8
     run_on:
       - rhel87-small
diff --git a/.evergreen/scripts/generate_config.py b/.evergreen/scripts/generate_config.py
index daec0841d5..de9600a782 100644
--- a/.evergreen/scripts/generate_config.py
+++ b/.evergreen/scripts/generate_config.py
@@ -128,7 +128,8 @@ def get_encryption_expansions(encryption):
     ):
         expansions = get_encryption_expansions(encryption)
         display_name = get_variant_name(encryption, host, **expansions)
-        tasks = [".test-non-standard", ".test-min-deps"]
+        # TODO: PYTHON-5612
+        tasks = [".test-non-standard !.pypy", ".test-min-deps"]
         if host != "rhel8":
             tasks = [".test-non-standard !.pypy"]
         variant = create_variant(
@@ -147,7 +148,7 @@ def get_encryption_expansions(encryption):
     expansions = get_encryption_expansions(encryption)
     display_name = get_variant_name(encryption, host, **expansions)
     variant = create_variant(
-        [".test-non-standard"],
+        [".test-non-standard !.pypy"],  # TODO: PYTHON-5612
         display_name,
         host=host,
         expansions=expansions,