diff --git a/docs/news.rst b/docs/news.rst
index 52e86e6d..df277259 100644
--- a/docs/news.rst
+++ b/docs/news.rst
@@ -3,6 +3,9 @@ Release Notes
 
 **UNRELEASED**
 
+- Fixed ``wheel pack --build-number`` accepting build tags that are invalid in a
+  wheel file name (not starting with a digit, or containing ``-``), the same
+  validation ``wheel tags --build`` already performs
 - Fixed the macOS platform-tag warning always using the plural "these files"
   wording, even when only a single library required a higher deployment target
   (`#697 <https://github.com/pypa/wheel/pull/697>`_)
diff --git a/src/wheel/_commands/__init__.py b/src/wheel/_commands/__init__.py
index 7931c786..0ebddc06 100644
--- a/src/wheel/_commands/__init__.py
+++ b/src/wheel/_commands/__init__.py
@@ -102,7 +102,9 @@ def parser() -> argparse.ArgumentParser:
         help="Directory to store the wheel (default %(default)s)",
     )
     repack_parser.add_argument(
-        "--build-number", help="Build tag to use in the wheel name"
+        "--build-number",
+        type=parse_build_tag,
+        help="Build tag to use in the wheel name",
     )
     repack_parser.add_argument(
         "--local-version", help="Local version identifier to add or replace"
diff --git a/tests/commands/test_pack.py b/tests/commands/test_pack.py
index e25bbeb3..cbbf3112 100644
--- a/tests/commands/test_pack.py
+++ b/tests/commands/test_pack.py
@@ -7,6 +7,7 @@
 from email.message import Message
 from email.parser import BytesParser
 from io import StringIO
+from subprocess import CalledProcessError
 from zipfile import Path, ZipFile
 
 import pytest
@@ -224,3 +225,33 @@ def test_pack_local_version_rejects_invalid(
 
     assert returncode == 1
     assert "!invalid" in stderr.getvalue()
+
+
+@pytest.mark.parametrize(
+    "build_tag, error",
+    [
+        pytest.param("foo", "build tag must begin with a digit", id="digitstart"),
+        pytest.param("1-f", "invalid character ('-') in build tag", id="hyphen"),
+    ],
+)
+def test_pack_invalid_build_tag(
+    tmp_path_factory: TempPathFactory, tmp_path: Path, build_tag: str, error: str
+) -> None:
+    unpack_dir = tmp_path_factory.mktemp("wheeldir")
+    with ZipFile(TESTWHEEL_PATH) as zf:
+        zf.extractall(unpack_dir)
+
+    with pytest.raises(CalledProcessError) as exc_info:
+        run_command(
+            "pack",
+            "--dest",
+            tmp_path,
+            unpack_dir,
+            "--build-number",
+            build_tag,
+            catch_systemexit=False,
+        )
+
+    exc = exc_info.value
+    assert exc.returncode == 2
+    assert f"error: argument --build-number: {error}" in exc.stderr