diff --git a/core/lib/Drupal/Core/Extension/InfoParserDynamic.php b/core/lib/Drupal/Core/Extension/InfoParserDynamic.php
index b255c02a01..8868f296e6 100644
--- a/core/lib/Drupal/Core/Extension/InfoParserDynamic.php
+++ b/core/lib/Drupal/Core/Extension/InfoParserDynamic.php
@@ -79,11 +79,19 @@ public function parse($filename) {
         }
         // 'core_version_requirement' can not be used to specify Drupal 8
         // versions before 8.7.7 because these versions do not use the
-        // 'core_version_requirement' key. Do not throw the exception if the
-        // constraint also is satisfied by 8.0.0-alpha1 to allow constraints
-        // such as '^8' or '^8 || ^9'.
-        if ($supports_pre_core_version_requirement_version && !static::satisfies('8.0.0-alpha1', $parsed_info['core_version_requirement'])) {
-          throw new InfoParserException("The 'core_version_requirement' can not be used to specify compatibility for a specific version before " . static::FIRST_CORE_VERSION_REQUIREMENT_SUPPORTED_VERSION . " in $filename");
+        // 'core_version_requirement' key.
+        if ($supports_pre_core_version_requirement_version) {
+          // Do not throw the exception if the constraint also is satisfied by
+          // 8.0.0-alpha1 to allow constraints such as '^8' or '^8 || ^9'.
+          if (!static::satisfies('8.0.0-alpha1', $parsed_info['core_version_requirement'])) {
+            throw new InfoParserException("The 'core_version_requirement' can not be used to specify compatibility for a specific version before " . static::FIRST_CORE_VERSION_REQUIREMENT_SUPPORTED_VERSION . " in $filename");
+          }
+          else {
+            if (!isset($parsed_info['core'])) {
+              throw new InfoParserException("If the 'core_version_requirement' specifies compatibility with all versions of Drupal 8 like '^8' the 'core: 8.x' must also be set in $filename");
+            }
+          }
+
         }
       }
 
diff --git a/core/modules/system/tests/modules/system_core_semver_test/system_core_semver_test.info.yml b/core/modules/system/tests/modules/system_core_semver_test/system_core_semver_test.info.yml
index 47eec87f48..e3501a5f0b 100644
--- a/core/modules/system/tests/modules/system_core_semver_test/system_core_semver_test.info.yml
+++ b/core/modules/system/tests/modules/system_core_semver_test/system_core_semver_test.info.yml
@@ -3,4 +3,4 @@ type: module
 description: 'Support module for testing core using semver.'
 package: Testing
 version: 1.0.0
-core_version_requirement: ^8
+core_version_requirement: ^8.7.7
diff --git a/core/modules/system/tests/modules/update_test_semver_update_n/update_test_semver_update_n.info.yml b/core/modules/system/tests/modules/update_test_semver_update_n/update_test_semver_update_n.info.yml
index 74e908530d..86bdbd3471 100644
--- a/core/modules/system/tests/modules/update_test_semver_update_n/update_test_semver_update_n.info.yml
+++ b/core/modules/system/tests/modules/update_test_semver_update_n/update_test_semver_update_n.info.yml
@@ -3,4 +3,4 @@ type: module
 description: 'Support module for update testing with core semver value.'
 package: Testing
 version: VERSION
-core_version_requirement: ^8
+core_version_requirement: ^8.7.7
diff --git a/core/modules/system/tests/themes/test_core_semver/test_core_semver.info.yml b/core/modules/system/tests/themes/test_core_semver/test_core_semver.info.yml
index 4645badc2a..d58c91bd65 100644
--- a/core/modules/system/tests/themes/test_core_semver/test_core_semver.info.yml
+++ b/core/modules/system/tests/themes/test_core_semver/test_core_semver.info.yml
@@ -2,4 +2,4 @@ name: 'Theme test with semver core version'
 type: theme
 description: 'Test theme which has semver core version.'
 version: VERSION
-core_version_requirement: ^8 || ^9
+core_version_requirement: ^8.7.7 || ^9
diff --git a/core/tests/Drupal/Tests/Core/Extension/InfoParserUnitTest.php b/core/tests/Drupal/Tests/Core/Extension/InfoParserUnitTest.php
index 1af2972383..a15d01b330 100644
--- a/core/tests/Drupal/Tests/Core/Extension/InfoParserUnitTest.php
+++ b/core/tests/Drupal/Tests/Core/Extension/InfoParserUnitTest.php
@@ -381,7 +381,7 @@ public function testInfoParserCommonInfo() {
    *
    * @dataProvider providerCoreIncompatibility
    */
-  public function testCoreIncompatibility($test_case, $constraint, $expected) {
+  public function testCoreIncompatibility($test_case, $constraint, $include_core, $expected) {
     $core_incompatibility = <<<CORE_INCOMPATIBILITY
 core_version_requirement: $constraint
 name: common_test
@@ -392,6 +392,15 @@ public function testCoreIncompatibility($test_case, $constraint, $expected) {
 double_colon: dummyClassName::method
 CORE_INCOMPATIBILITY;
 
+    if ($include_core) {
+      $core_incompatibility .= <<<CORE_INCOMPATIBILITY
+
+core: 8.x
+CORE_INCOMPATIBILITY;
+
+    }
+
+
     vfsStream::setup('modules');
     foreach (['1', '2'] as $file_delta) {
       $filename = "core_incompatible-$test_case-$file_delta.info.txt";
@@ -417,27 +426,32 @@ public function providerCoreIncompatibility() {
       'next_minor' => [
         'next_minor',
         "^$major.$next_minor",
+        FALSE,
         TRUE,
       ],
       'current_major_next_major' => [
         'current_major_next_major',
         "^$major || ^$next_major",
+        TRUE,
         FALSE,
       ],
       'previous_major_next_major' => [
         'previous_major_next_major',
         "^1 || ^$next_major",
+        FALSE,
         TRUE,
       ],
       'invalid' => [
         'invalid',
         'this-string-is-invalid',
+        FALSE,
         TRUE,
       ],
       'current_minor' => [
         'current_minor',
         "~$major.$minor",
         FALSE,
+        FALSE,
       ],
     ];
   }