diff --git a/src/lightning/fabric/plugins/precision/amp.py b/src/lightning/fabric/plugins/precision/amp.py
index f766292cb9142..36326bfaa001f 100644
--- a/src/lightning/fabric/plugins/precision/amp.py
+++ b/src/lightning/fabric/plugins/precision/amp.py
@@ -42,7 +42,7 @@ def __init__(
         scaler: Optional[torch.cuda.amp.GradScaler] = None,
     ) -> None:
         if precision not in ("16-mixed", "bf16-mixed"):
-            raise ValueError(f"`{type(self).__name__}(precision={precision!r})` must be '16-mixed' or 'bf16-mixed'")
+            raise ValueError(f"Passed `{type(self).__name__}(precision={precision!r})`. Precision must be '16-mixed' or 'bf16-mixed'")
 
         self.precision = cast(Literal["16-mixed", "bf16-mixed"], str(precision))
         if scaler is None and self.precision == "16-mixed":
diff --git a/src/lightning/pytorch/plugins/precision/amp.py b/src/lightning/pytorch/plugins/precision/amp.py
index a5fbf976b7340..119502fbcd75b 100644
--- a/src/lightning/pytorch/plugins/precision/amp.py
+++ b/src/lightning/pytorch/plugins/precision/amp.py
@@ -41,7 +41,7 @@ def __init__(
         scaler: Optional[torch.cuda.amp.GradScaler] = None,
     ) -> None:
         if precision not in ("16-mixed", "bf16-mixed"):
-            raise ValueError(f"`{type(self).__name__}(precision={precision!r})` must be '16-mixed' or 'bf16-mixed'")
+            raise ValueError(f"`Passed `{type(self).__name__}(precision={precision!r})`. Precision must be '16-mixed' or 'bf16-mixed'")
 
         self.precision = cast(Literal["16-mixed", "bf16-mixed"], str(precision))
         if scaler is None and self.precision == "16-mixed":
diff --git a/tests/tests_fabric/plugins/precision/test_amp.py b/tests/tests_fabric/plugins/precision/test_amp.py
index 6d35e040b4c43..fd83ef223e96a 100644
--- a/tests/tests_fabric/plugins/precision/test_amp.py
+++ b/tests/tests_fabric/plugins/precision/test_amp.py
@@ -91,16 +91,19 @@ def test_amp_precision_parameter_validation():
     MixedPrecision("bf16-mixed", "cpu")
 
     with pytest.raises(
-        ValueError, match=re.escape("`MixedPrecision(precision='16')` must be '16-mixed' or 'bf16-mixed'")
+        ValueError,
+        match=re.escape("Passed `MixedPrecision(precision='16')`. Precision must be '16-mixed' or 'bf16-mixed'"),
     ):
         MixedPrecision("16", "cpu")
 
     with pytest.raises(
-        ValueError, match=re.escape("`MixedPrecision(precision=16)` must be '16-mixed' or 'bf16-mixed'")
+        ValueError,
+        match=re.escape("Passed `MixedPrecision(precision=16)`. Precision must be '16-mixed' or 'bf16-mixed'"),
     ):
         MixedPrecision(16, "cpu")
 
     with pytest.raises(
-        ValueError, match=re.escape("`MixedPrecision(precision='bf16')` must be '16-mixed' or 'bf16-mixed'")
+        ValueError,
+        match=re.escape("Passed `MixedPrecision(precision='bf16')`. Precision must be '16-mixed' or 'bf16-mixed'"),
     ):
         MixedPrecision("bf16", "cpu")
diff --git a/tests/tests_pytorch/plugins/test_amp_plugins.py b/tests/tests_pytorch/plugins/test_amp_plugins.py
index 65724ff938015..b9f9bd3bcb64e 100644
--- a/tests/tests_pytorch/plugins/test_amp_plugins.py
+++ b/tests/tests_pytorch/plugins/test_amp_plugins.py
@@ -201,16 +201,21 @@ def test_amp_precision_plugin_parameter_validation():
     MixedPrecisionPlugin("bf16-mixed", "cpu")
 
     with pytest.raises(
-        ValueError, match=re.escape("`MixedPrecisionPlugin(precision='16')` must be '16-mixed' or 'bf16-mixed'")
+        ValueError,
+        match=re.escape("Passed `MixedPrecisionPlugin(precision='16')`. Precision must be '16-mixed' or 'bf16-mixed'"),
     ):
         MixedPrecisionPlugin("16", "cpu")
 
     with pytest.raises(
-        ValueError, match=re.escape("`MixedPrecisionPlugin(precision=16)` must be '16-mixed' or 'bf16-mixed'")
+        ValueError,
+        match=re.escape("Passed `MixedPrecisionPlugin(precision=16)`. Precision must be '16-mixed' or 'bf16-mixed'"),
     ):
         MixedPrecisionPlugin(16, "cpu")
 
     with pytest.raises(
-        ValueError, match=re.escape("`MixedPrecisionPlugin(precision='bf16')` must be '16-mixed' or 'bf16-mixed'")
+        ValueError,
+        match=re.escape(
+            "Passed `MixedPrecisionPlugin(precision='bf16')`. Precision must be '16-mixed' or 'bf16-mixed'"
+        ),
     ):
         MixedPrecisionPlugin("bf16", "cpu")