diff --git a/mypy/build.py b/mypy/build.py
index 499f027d8fae..cbf7b0b6f5b5 100644
--- a/mypy/build.py
+++ b/mypy/build.py
@@ -2449,7 +2449,9 @@ def find_module_and_diagnose(manager: BuildManager,
         # otherwise updating mypy can silently result in new false
         # negatives.
         global_ignore_missing_imports = manager.options.ignore_missing_imports
-        if top_level in legacy_bundled_packages and global_ignore_missing_imports:
+        if (top_level in legacy_bundled_packages
+                and global_ignore_missing_imports
+                and not options.ignore_missing_imports_per_module):
             ignore_missing_imports = False
 
         if skip_diagnose:
diff --git a/mypy/options.py b/mypy/options.py
index 099d998f2e46..aa92b1cea9ff 100644
--- a/mypy/options.py
+++ b/mypy/options.py
@@ -82,6 +82,8 @@ def __init__(self) -> None:
         self.no_silence_site_packages = False
         self.no_site_packages = False
         self.ignore_missing_imports = False
+        # Is ignore_missing_imports set in a per-module section
+        self.ignore_missing_imports_per_module = False
         self.follow_imports = 'normal'  # normal|silent|skip|error
         # Whether to respect the follow_imports setting even for stub files.
         # Intended to be used for disabling specific stubs.
@@ -325,6 +327,10 @@ def apply_changes(self, changes: Dict[str, object]) -> 'Options':
         replace_object_state(new_options, self, copy_dict=True)
         for key, value in changes.items():
             setattr(new_options, key, value)
+        if changes.get("ignore_missing_imports"):
+            # This is the only option for which a per-module and a global
+            # option sometimes beheave differently.
+            new_options.ignore_missing_imports_per_module = True
         return new_options
 
     def build_per_module_cache(self) -> None:
diff --git a/test-data/unit/check-modules.test b/test-data/unit/check-modules.test
index d06dfb413275..643488ec4158 100644
--- a/test-data/unit/check-modules.test
+++ b/test-data/unit/check-modules.test
@@ -3011,7 +3011,6 @@ certifi.x  # E: Expression has type "Any"
 certifi.x  # E: Expression has type "Any"
 1()  # E: "int" not callable
 
-
 [case testDoNotLimitImportErrorVolume]
 # flags: --disallow-any-expr --soft-error-limit=3
 import xyz1  # E: Cannot find implementation or library stub for module named "xyz1" \
@@ -3064,3 +3063,34 @@ certifi.x  # E: Expression has type "Any"
 certifi.x  # E: Expression has type "Any"
 certifi.x  # E: Expression has type "Any"
 certifi.x  # E: Expression has type "Any"
+
+[case testIgnoreErrorFromMissingStubs1]
+# flags: --config-file tmp/pyproject.toml
+import certifi
+from foobar1 import x
+import foobar2
+[file pyproject.toml]
+\[tool.mypy]
+ignore_missing_imports = true
+\[[tool.mypy.overrides]]
+module = "certifi"
+ignore_missing_imports = true
+\[[tool.mypy.overrides]]
+module = "foobar1"
+ignore_missing_imports = true
+
+[case testIgnoreErrorFromMissingStubs2]
+# flags: --config-file tmp/pyproject.toml
+import certifi
+from foobar1 import x
+import foobar2  # E: Cannot find implementation or library stub for module named "foobar2" \
+                # N: See https://mypy.readthedocs.io/en/stable/running_mypy.html#missing-imports
+[file pyproject.toml]
+\[tool.mypy]
+ignore_missing_imports = false
+\[[tool.mypy.overrides]]
+module = "certifi"
+ignore_missing_imports = true
+\[[tool.mypy.overrides]]
+module = "foobar1"
+ignore_missing_imports = true