diff --git a/doc/source/whatsnew/v1.6.0.rst b/doc/source/whatsnew/v1.6.0.rst
index ee5085fd9ad89..975909686c28f 100644
--- a/doc/source/whatsnew/v1.6.0.rst
+++ b/doc/source/whatsnew/v1.6.0.rst
@@ -121,7 +121,7 @@ Categorical
 
 Datetimelike
 ^^^^^^^^^^^^
--
+- Bug in :func:`pandas.infer_freq`, raising ``TypeError`` when inferred on :class:`RangeIndex` (:issue:`47084`)
 -
 
 Timedelta
diff --git a/pandas/tests/tseries/frequencies/test_inference.py b/pandas/tests/tseries/frequencies/test_inference.py
index 396cb950bd8b2..ea9a09ff2d65c 100644
--- a/pandas/tests/tseries/frequencies/test_inference.py
+++ b/pandas/tests/tseries/frequencies/test_inference.py
@@ -358,9 +358,16 @@ def test_non_datetime_index2():
 
 
 @pytest.mark.parametrize(
-    "idx", [tm.makeIntIndex(10), tm.makeFloatIndex(10), tm.makePeriodIndex(10)]
+    "idx",
+    [
+        tm.makeIntIndex(10),
+        tm.makeFloatIndex(10),
+        tm.makePeriodIndex(10),
+        tm.makeRangeIndex(10),
+    ],
 )
 def test_invalid_index_types(idx):
+    # see gh-48439
     msg = "|".join(
         [
             "cannot infer freq from a non-convertible",
diff --git a/pandas/tseries/frequencies.py b/pandas/tseries/frequencies.py
index 3edabc7c089e1..ce62a15eda367 100644
--- a/pandas/tseries/frequencies.py
+++ b/pandas/tseries/frequencies.py
@@ -160,6 +160,7 @@ def infer_freq(index, warn: bool = True) -> str | None:
         Float64Index,
         Index,
         Int64Index,
+        RangeIndex,
     )
 
     if isinstance(index, ABCSeries):
@@ -190,7 +191,7 @@ def infer_freq(index, warn: bool = True) -> str | None:
         return inferer.get_freq()
 
     if isinstance(index, Index) and not isinstance(index, DatetimeIndex):
-        if isinstance(index, (Int64Index, Float64Index)):
+        if isinstance(index, (Int64Index, Float64Index, RangeIndex)):
             raise TypeError(
                 f"cannot infer freq from a non-convertible index type {type(index)}"
             )