diff --git a/pandas/tseries/frequencies.py b/pandas/tseries/frequencies.py
index caa34a067ac69..a573584b74db9 100644
--- a/pandas/tseries/frequencies.py
+++ b/pandas/tseries/frequencies.py
@@ -140,7 +140,10 @@ def infer_freq(
     >>> pd.infer_freq(idx)
     'D'
     """
-    from pandas.core.api import DatetimeIndex
+    from pandas.core.api import (
+        DatetimeIndex,
+        Index,
+    )
 
     if isinstance(index, ABCSeries):
         values = index._values
@@ -169,10 +172,15 @@ def infer_freq(
         inferer = _TimedeltaFrequencyInferer(index)
         return inferer.get_freq()
 
-    elif is_numeric_dtype(index.dtype):
-        raise TypeError(
-            f"cannot infer freq from a non-convertible index of dtype {index.dtype}"
-        )
+    if isinstance(index, Index) and not isinstance(index, DatetimeIndex):
+        if is_numeric_dtype(index.dtype):
+            raise TypeError(
+                f"cannot infer freq from a non-convertible index of dtype {index.dtype}"
+            )
+        # error: Incompatible types in assignment (expression has type
+        # "Union[ExtensionArray, ndarray[Any, Any]]", variable has type
+        # "Union[DatetimeIndex, TimedeltaIndex, Series, DatetimeLikeArrayMixin]")
+        index = index._values  # type: ignore[assignment]
 
     if not isinstance(index, DatetimeIndex):
         index = DatetimeIndex(index)
@@ -622,4 +630,4 @@ def _is_weekly(rule: str) -> bool:
     "is_subperiod",
     "is_superperiod",
     "to_offset",
-]
+]
\ No newline at end of file