diff --git a/CHANGELOG.md b/CHANGELOG.md
index d0af296fd8aa..96ece1aa44f9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -43,6 +43,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Escaping in the `filter` parameter in generated URLs
   (<https://github.com/opencv/cvat/issues/5566>)
 - Rotation property lost during saving a mutable attribute (<https://github.com/opencv/cvat/pull/5968>)
+- Server micro version support check in SDK/CLI (<https://github.com/opencv/cvat/pull/5991>)
 
 ### Security
 - TDB
diff --git a/cvat-sdk/cvat_sdk/core/client.py b/cvat-sdk/cvat_sdk/core/client.py
index eafa21f7612d..1db2de999bd6 100644
--- a/cvat-sdk/cvat_sdk/core/client.py
+++ b/cvat-sdk/cvat_sdk/core/client.py
@@ -13,6 +13,7 @@
 from typing import Any, Dict, Iterator, Optional, Sequence, Tuple, TypeVar
 
 import attrs
+import packaging.specifiers as specifiers
 import packaging.version as pv
 import platformdirs
 import urllib3
@@ -253,25 +254,29 @@ def check_server_version(self, fail_if_unsupported: Optional[bool] = None) -> No
                 raise IncompatibleVersionException(msg)
             return
 
-        sdk_version = pv.Version(VERSION)
-
-        # We only check base version match. Micro releases and fixes do not affect
-        # API compatibility in general.
-        if all(
-            server_version.base_version != sv.base_version for sv in self.SUPPORTED_SERVER_VERSIONS
+        if not any(
+            self._is_version_compatible(server_version, supported_version)
+            for supported_version in self.SUPPORTED_SERVER_VERSIONS
         ):
             msg = (
                 "Server version '%s' is not compatible with SDK version '%s'. "
                 "Some SDK functions may not work properly with this server. "
                 "You can continue using this SDK, or you can "
                 "try to update with 'pip install cvat-sdk'."
-            ) % (server_version, sdk_version)
+            ) % (server_version, pv.Version(VERSION))
             self.logger.warning(msg)
             if fail_if_unsupported:
                 raise IncompatibleVersionException(msg)
 
+    def _is_version_compatible(self, current: pv.Version, target: pv.Version) -> bool:
+        # Check for (major, minor) compatibility.
+        # Micro releases and fixes do not affect API compatibility in general.
+        epoch = f"{target.epoch}!" if target.epoch else ""  # 1.0 ~= 0!1.0 is false
+        return current in specifiers.Specifier(
+            f"~= {epoch}{target.major}.{target.minor}.{target.micro}"
+        )
+
     def get_server_version(self) -> pv.Version:
-        # TODO: allow to use this endpoint unauthorized
         (about, _) = self.api_client.server_api.retrieve_about()
         return pv.Version(about.version)
 
diff --git a/tests/python/sdk/test_client.py b/tests/python/sdk/test_client.py
index 58bfa310c97f..4c3a63837f89 100644
--- a/tests/python/sdk/test_client.py
+++ b/tests/python/sdk/test_client.py
@@ -5,7 +5,7 @@
 import io
 from contextlib import ExitStack
 from logging import Logger
-from typing import Tuple
+from typing import List, Tuple
 
 import packaging.version as pv
 import pytest
@@ -160,6 +160,51 @@ def mocked_version(_):
     assert "Server version '0' is not compatible with SDK version" in logger_stream.getvalue()
 
 
+@pytest.mark.parametrize(
+    "server_version, supported_versions, expect_supported",
+    [
+        # Currently, it is ~=, as defined in https://peps.python.org/pep-0440/
+        ("3.2", ["2.0"], False),
+        ("2", ["2.1"], False),
+        ("2.1", ["2.1"], True),
+        ("2.1a", ["2.1"], False),
+        ("2.1.post1", ["2.1"], True),
+        ("2.1", ["2.1.pre1"], True),
+        ("2.1.1", ["2.1"], True),
+        ("2.2", ["2.1"], False),
+        ("2.2", ["2.1.0", "2.3"], False),
+        ("2.2", ["2.1", "2.2", "2.3"], True),
+        ("2.2.post1", ["2.1", "2.2", "2.3"], True),
+        ("2.2.pre1", ["2.1", "2.2", "2.3"], False),
+        ("2.2", ["2.3"], False),
+        ("2.1.0.dev123", ["2.1.post2"], False),
+        ("1!1.3", ["2.1"], False),
+        ("1!1.3.1", ["2.1", "1!1.3"], True),
+        ("1!1.1.dev12", ["1!1.1"], False),
+    ],
+)
+def test_can_check_server_version_compatibility(
+    fxt_logger: Tuple[Logger, io.StringIO],
+    monkeypatch: pytest.MonkeyPatch,
+    server_version: str,
+    supported_versions: List[str],
+    expect_supported: bool,
+):
+    logger, _ = fxt_logger
+
+    monkeypatch.setattr(Client, "get_server_version", lambda _: pv.Version(server_version))
+    monkeypatch.setattr(
+        Client, "SUPPORTED_SERVER_VERSIONS", [pv.Version(v) for v in supported_versions]
+    )
+    config = Config(allow_unsupported_server=False)
+
+    with ExitStack() as es:
+        if not expect_supported:
+            es.enter_context(pytest.raises(IncompatibleVersionException))
+
+        Client(url=BASE_URL, logger=logger, config=config, check_server_version=True)
+
+
 @pytest.mark.parametrize("verify", [True, False])
 def test_can_control_ssl_verification_with_config(verify: bool):
     config = Config(verify_ssl=verify)