diff --git a/news/9206.feature.rst b/news/9206.feature.rst
new file mode 100644
index 000000000..90cd2cf99
--- /dev/null
+++ b/news/9206.feature.rst
@@ -0,0 +1,3 @@
+``pip wheel`` now verifies the built wheel contains valid metadata, and can be
+installed by a subsequent ``pip install``. This can be disabled with
+``--no-verify``.
diff --git a/src/pip/_internal/commands/install.py b/src/pip/_internal/commands/install.py
index a1167887f..e303adf86 100644
--- a/src/pip/_internal/commands/install.py
+++ b/src/pip/_internal/commands/install.py
@@ -343,6 +343,7 @@ class InstallCommand(RequirementCommand):
             _, build_failures = build(
                 reqs_to_build,
                 wheel_cache=wheel_cache,
+                verify=True,
                 build_options=[],
                 global_options=[],
             )
diff --git a/src/pip/_internal/commands/wheel.py b/src/pip/_internal/commands/wheel.py
index 13dad544c..28918fa74 100644
--- a/src/pip/_internal/commands/wheel.py
+++ b/src/pip/_internal/commands/wheel.py
@@ -77,6 +77,14 @@ class WheelCommand(RequirementCommand):
         self.cmd_opts.add_option(cmdoptions.build_dir())
         self.cmd_opts.add_option(cmdoptions.progress_bar())
 
+        self.cmd_opts.add_option(
+            '--no-verify',
+            dest='no_verify',
+            action='store_true',
+            default=False,
+            help="Don't verify if built wheel is valid.",
+        )
+
         self.cmd_opts.add_option(
             '--global-option',
             dest='global_options',
@@ -162,6 +170,7 @@ class WheelCommand(RequirementCommand):
         build_successes, build_failures = build(
             reqs_to_build,
             wheel_cache=wheel_cache,
+            verify=(not options.no_verify),
             build_options=options.build_options or [],
             global_options=options.global_options or [],
         )
diff --git a/src/pip/_internal/wheel_builder.py b/src/pip/_internal/wheel_builder.py
index e315fe111..c23ee1ba7 100644
--- a/src/pip/_internal/wheel_builder.py
+++ b/src/pip/_internal/wheel_builder.py
@@ -5,8 +5,15 @@ import logging
 import os.path
 import re
 import shutil
+import zipfile
 
+from pip._vendor.packaging.utils import canonicalize_name, canonicalize_version
+from pip._vendor.packaging.version import InvalidVersion, Version
+from pip._vendor.pkg_resources import Distribution
+
+from pip._internal.exceptions import InvalidWheelFilename, UnsupportedWheel
 from pip._internal.models.link import Link
+from pip._internal.models.wheel import Wheel
 from pip._internal.operations.build.wheel import build_wheel_pep517
 from pip._internal.operations.build.wheel_legacy import build_wheel_legacy
 from pip._internal.utils.logging import indent_log
@@ -16,6 +23,7 @@ from pip._internal.utils.subprocess import call_subprocess
 from pip._internal.utils.temp_dir import TempDirectory
 from pip._internal.utils.typing import MYPY_CHECK_RUNNING
 from pip._internal.utils.urls import path_to_url
+from pip._internal.utils.wheel import pkg_resources_distribution_for_wheel
 from pip._internal.vcs import vcs
 
 if MYPY_CHECK_RUNNING:
@@ -163,9 +171,49 @@ def _always_true(_):
     return True
 
 
+def _get_metadata_version(dist):
+    # type: (Distribution) -> Optional[Version]
+    for line in dist.get_metadata_lines(dist.PKG_INFO):
+        if line.lower().startswith("metadata-version:"):
+            value = line.split(":", 1)[-1].strip()
+            try:
+                return Version(value)
+            except InvalidVersion:
+                msg = "Invalid Metadata-Version: {}".format(value)
+                raise UnsupportedWheel(msg)
+    raise UnsupportedWheel("Missing Metadata-Version")
+
+
+def _verify_one(req, wheel_path):
+    # type: (InstallRequirement, str) -> None
+    canonical_name = canonicalize_name(req.name)
+    w = Wheel(os.path.basename(wheel_path))
+    if canonicalize_name(w.name) != canonical_name:
+        raise InvalidWheelFilename(
+            "Wheel has unexpected file name: expected {!r}, "
+            "got {!r}".format(canonical_name, w.name),
+        )
+    with zipfile.ZipFile(wheel_path, allowZip64=True) as zf:
+        dist = pkg_resources_distribution_for_wheel(
+            zf, canonical_name, wheel_path,
+        )
+    if canonicalize_version(dist.version) != canonicalize_version(w.version):
+        raise InvalidWheelFilename(
+            "Wheel has unexpected file name: expected {!r}, "
+            "got {!r}".format(dist.version, w.version),
+        )
+    if (_get_metadata_version(dist) >= Version("1.2")
+            and not isinstance(dist.parsed_version, Version)):
+        raise UnsupportedWheel(
+            "Metadata 1.2 mandates PEP 440 version, "
+            "but {!r} is not".format(dist.version)
+        )
+
+
 def _build_one(
     req,  # type: InstallRequirement
     output_dir,  # type: str
+    verify,  # type: bool
     build_options,  # type: List[str]
     global_options,  # type: List[str]
 ):
@@ -185,9 +233,16 @@ def _build_one(
 
     # Install build deps into temporary directory (PEP 518)
     with req.build_env:
-        return _build_one_inside_env(
+        wheel_path = _build_one_inside_env(
             req, output_dir, build_options, global_options
         )
+    if wheel_path and verify:
+        try:
+            _verify_one(req, wheel_path)
+        except (InvalidWheelFilename, UnsupportedWheel) as e:
+            logger.warning("Built wheel for %s is invalid: %s", req.name, e)
+            return None
+    return wheel_path
 
 
 def _build_one_inside_env(
@@ -260,6 +315,7 @@ def _clean_one_legacy(req, global_options):
 def build(
     requirements,  # type: Iterable[InstallRequirement]
     wheel_cache,  # type: WheelCache
+    verify,  # type: bool
     build_options,  # type: List[str]
     global_options,  # type: List[str]
 ):
@@ -283,7 +339,7 @@ def build(
         for req in requirements:
             cache_dir = _get_cache_dir(req, wheel_cache)
             wheel_file = _build_one(
-                req, cache_dir, build_options, global_options
+                req, cache_dir, verify, build_options, global_options
             )
             if wheel_file:
                 # Update the link for this.