diff --git a/src/pytorch_lightning/plugins/precision/deepspeed.py b/src/pytorch_lightning/plugins/precision/deepspeed.py
index 4cc12de400ef44..0e0b2d833647cc 100644
--- a/src/pytorch_lightning/plugins/precision/deepspeed.py
+++ b/src/pytorch_lightning/plugins/precision/deepspeed.py
@@ -22,11 +22,9 @@
 from pytorch_lightning.utilities import GradClipAlgorithmType
 from pytorch_lightning.utilities.enums import PrecisionType
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
-from pytorch_lightning.utilities.imports import _RequirementAvailable
 from pytorch_lightning.utilities.model_helpers import is_overridden
 from pytorch_lightning.utilities.warnings import WarningCache
 
-_DEEPSPEED_GREATER_EQUAL_0_6 = _RequirementAvailable("deepspeed>=0.6.0")
 if TYPE_CHECKING:
     if pl.strategies.deepspeed._DEEPSPEED_AVAILABLE:
         import deepspeed
@@ -52,12 +50,6 @@ class DeepSpeedPrecisionPlugin(PrecisionPlugin):
     """
 
     def __init__(self, precision: Union[str, int], amp_type: str, amp_level: Optional[str] = None) -> None:
-        if precision == PrecisionType.BFLOAT and not _DEEPSPEED_GREATER_EQUAL_0_6:
-            raise MisconfigurationException(
-                f"`Trainer(strategy='deepspeed', precision={precision!r})` is not supported"
-                " with `deepspeed < v0.6`. Please upgrade it using `pip install -U deepspeed`."
-            )
-
         supported_precision = (PrecisionType.HALF, PrecisionType.FLOAT, PrecisionType.BFLOAT, PrecisionType.MIXED)
         if precision not in supported_precision:
             raise ValueError(
diff --git a/tests/tests_pytorch/plugins/precision/test_deepspeed_precision.py b/tests/tests_pytorch/plugins/precision/test_deepspeed_precision.py
index 8a68f7c73209b2..a4698e7c19c97c 100644
--- a/tests/tests_pytorch/plugins/precision/test_deepspeed_precision.py
+++ b/tests/tests_pytorch/plugins/precision/test_deepspeed_precision.py
@@ -11,20 +11,11 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from unittest import mock
-
 import pytest
 
 from pytorch_lightning.plugins.precision.deepspeed import DeepSpeedPrecisionPlugin
-from pytorch_lightning.utilities.exceptions import MisconfigurationException
 
 
 def test_invalid_precision_with_deepspeed_precision():
     with pytest.raises(ValueError, match="is not supported. `precision` must be one of"):
         DeepSpeedPrecisionPlugin(precision=64, amp_type="native")
-
-
-@mock.patch("pytorch_lightning.plugins.precision.deepspeed._DEEPSPEED_GREATER_EQUAL_0_6", False)
-def test_incompatible_bfloat16_raises_error_with_deepspeed_version():
-    with pytest.raises(MisconfigurationException, match="is not supported with `deepspeed < v0.6`"):
-        DeepSpeedPrecisionPlugin(precision="bf16", amp_type="native")