diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index a9140fa20ceef..da8d88fe6cbb1 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -174,6 +174,7 @@ Indexing
 - Bug in assignment using a reverse slicer (:issue:`26939`)
 - Bug in reindexing a :meth:`PeriodIndex` with another type of index that contained a `Period` (:issue:`28323`) (:issue:`28337`)
 - Fix assignment of column via `.loc` with numpy non-ns datetime type (:issue:`27395`)
+- Bug in :meth:`Float64Index.astype` where ``np.inf`` was not handled properly when casting to an integer dtype (:issue:`28475`)
 
 Missing
 ^^^^^^^
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index 2cdf73788dd9b..e83360dc701f3 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -5,6 +5,7 @@
 from pandas._libs import index as libindex
 from pandas.util._decorators import Appender, cache_readonly
 
+from pandas.core.dtypes.cast import astype_nansafe
 from pandas.core.dtypes.common import (
     is_bool,
     is_bool_dtype,
@@ -367,12 +368,11 @@ def astype(self, dtype, copy=True):
                 "values are required for conversion"
             ).format(dtype=dtype)
             raise TypeError(msg)
-        elif (
-            is_integer_dtype(dtype) and not is_extension_array_dtype(dtype)
-        ) and self.hasnans:
+        elif is_integer_dtype(dtype) and not is_extension_array_dtype(dtype):
             # TODO(jreback); this can change once we have an EA Index type
             # GH 13149
-            raise ValueError("Cannot convert NA to integer")
+            arr = astype_nansafe(self.values, dtype=dtype)
+            return Int64Index(arr)
         return super().astype(dtype, copy=copy)
 
     @Appender(_index_shared_docs["_convert_scalar_indexer"])
diff --git a/pandas/tests/indexes/interval/test_astype.py b/pandas/tests/indexes/interval/test_astype.py
index 863b8c9082f07..708cd8a4579e8 100644
--- a/pandas/tests/indexes/interval/test_astype.py
+++ b/pandas/tests/indexes/interval/test_astype.py
@@ -143,7 +143,7 @@ def test_subtype_integer(self, subtype):
         tm.assert_index_equal(result, expected)
 
         # raises with NA
-        msg = "Cannot convert NA to integer"
+        msg = r"Cannot convert non-finite values \(NA or inf\) to integer"
         with pytest.raises(ValueError, match=msg):
             index.insert(0, np.nan).astype(dtype)
 
diff --git a/pandas/tests/indexes/test_numeric.py b/pandas/tests/indexes/test_numeric.py
index f246307e63e3b..8bc9783694492 100644
--- a/pandas/tests/indexes/test_numeric.py
+++ b/pandas/tests/indexes/test_numeric.py
@@ -242,10 +242,17 @@ def test_astype(self):
         # GH 13149
         for dtype in ["int16", "int32", "int64"]:
             i = Float64Index([0, 1.1, np.NAN])
-            msg = "Cannot convert NA to integer"
+            msg = r"Cannot convert non-finite values \(NA or inf\) to integer"
             with pytest.raises(ValueError, match=msg):
                 i.astype(dtype)
 
+    def test_cannot_cast_inf_to_int(self):
+        idx = pd.Float64Index([1, 2, np.inf])
+
+        msg = r"Cannot convert non-finite values \(NA or inf\) to integer"
+        with pytest.raises(ValueError, match=msg):
+            idx.astype(int)
+
     def test_type_coercion_fail(self, any_int_dtype):
         # see gh-15832
         msg = "Trying to coerce float values to integers"