diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index ae2d054fe94fed..2d14b98a6f7797 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -59,6 +59,8 @@
     is_number,
     is_object_dtype,
     is_scalar,
+    is_signed_integer_dtype,
+    is_unsigned_integer_dtype,
 )
 from pandas.core.dtypes.dtypes import IntervalDtype
 from pandas.core.dtypes.missing import is_valid_na_for_dtype
@@ -340,8 +342,8 @@ def from_tuples(
     # "Union[IndexEngine, ExtensionEngine]" in supertype "Index"
     @cache_readonly
     def _engine(self) -> IntervalTree:  # type: ignore[override]
-        left = self._maybe_convert_i8(self.left)
-        right = self._maybe_convert_i8(self.right)
+        left = self._maybe_convert_to_64bit_if_numeric(self.left)
+        right = self._maybe_convert_to_64bit_if_numeric(self.right)
         return IntervalTree(left, right, closed=self.closed)
 
     def __contains__(self, key: Any) -> bool:
@@ -501,6 +503,18 @@ def _needs_i8_conversion(self, key) -> bool:
         i8_types = (Timestamp, Timedelta, DatetimeIndex, TimedeltaIndex)
         return isinstance(key, i8_types)
 
+    def _maybe_convert_to_64bit_if_numeric(self, key):
+        key = self._maybe_convert_i8(key)
+        dtype = key.dtype
+        if is_signed_integer_dtype(dtype) and dtype != "int64":
+            return key.astype(np.int64)
+        elif is_unsigned_integer_dtype(dtype) and dtype != "uint64":
+            return key.astype(np.uint64)
+        elif is_float_dtype(dtype) and dtype != "float64":
+            return key.astype(np.float64)
+        else:
+            return key
+
     def _maybe_convert_i8(self, key):
         """
         Maybe convert a given key to its equivalent i8 value(s). Used as a
diff --git a/pandas/tests/indexes/interval/test_constructors.py b/pandas/tests/indexes/interval/test_constructors.py
index 37e7bc04d5a2f9..140be64ea97858 100644
--- a/pandas/tests/indexes/interval/test_constructors.py
+++ b/pandas/tests/indexes/interval/test_constructors.py
@@ -19,11 +19,7 @@
 )
 import pandas._testing as tm
 from pandas.api.types import is_unsigned_integer_dtype
-from pandas.core.api import (
-    Float64Index,
-    Int64Index,
-    UInt64Index,
-)
+from pandas.core.api import NumericIndex
 from pandas.core.arrays import IntervalArray
 import pandas.core.common as com
 
@@ -44,9 +40,9 @@ class ConstructorTests:
         params=[
             ([3, 14, 15, 92, 653], np.int64),
             (np.arange(10, dtype="int64"), np.int64),
-            (Int64Index(range(-10, 11)), np.int64),
-            (UInt64Index(range(10, 31)), np.uint64),
-            (Float64Index(np.arange(20, 30, 0.5)), np.float64),
+            (NumericIndex(range(-10, 11), dtype=np.int64), np.int64),
+            (NumericIndex(range(10, 31), dtype=np.uint64), np.uint64),
+            (NumericIndex(np.arange(20, 30, 0.5), dtype=np.float64), np.float64),
             (date_range("20180101", periods=10), "<M8[ns]"),
             (
                 date_range("20180101", periods=10, tz="US/Eastern"),
@@ -74,10 +70,10 @@ def test_constructor(self, constructor, breaks_and_expected_subtype, closed, nam
     @pytest.mark.parametrize(
         "breaks, subtype",
         [
-            (Int64Index([0, 1, 2, 3, 4]), "float64"),
-            (Int64Index([0, 1, 2, 3, 4]), "datetime64[ns]"),
-            (Int64Index([0, 1, 2, 3, 4]), "timedelta64[ns]"),
-            (Float64Index([0, 1, 2, 3, 4]), "int64"),
+            (NumericIndex([0, 1, 2, 3, 4], dtype=np.int64), "float64"),
+            (NumericIndex([0, 1, 2, 3, 4], dtype=np.int64), "datetime64[ns]"),
+            (NumericIndex([0, 1, 2, 3, 4], dtype=np.int64), "timedelta64[ns]"),
+            (NumericIndex([0, 1, 2, 3, 4], dtype=np.float64), "int64"),
             (date_range("2017-01-01", periods=5), "int64"),
             (timedelta_range("1 day", periods=5), "int64"),
         ],
@@ -96,9 +92,9 @@ def test_constructor_dtype(self, constructor, breaks, subtype):
     @pytest.mark.parametrize(
         "breaks",
         [
-            Int64Index([0, 1, 2, 3, 4]),
-            UInt64Index([0, 1, 2, 3, 4]),
-            Float64Index([0, 1, 2, 3, 4]),
+            NumericIndex([0, 1, 2, 3, 4], dtype=np.int64),
+            NumericIndex([0, 1, 2, 3, 4], dtype=np.uint64),
+            NumericIndex([0, 1, 2, 3, 4], dtype=np.float64),
             date_range("2017-01-01", periods=5),
             timedelta_range("1 day", periods=5),
         ],
@@ -255,8 +251,8 @@ def test_mixed_float_int(self, left_subtype, right_subtype):
         right = np.arange(1, 10, dtype=right_subtype)
         result = IntervalIndex.from_arrays(left, right)
 
-        expected_left = Float64Index(left)
-        expected_right = Float64Index(right)
+        expected_left = NumericIndex(left, dtype=np.float64)
+        expected_right = NumericIndex(right, dtype=np.float64)
         expected_subtype = np.float64
 
         tm.assert_index_equal(result.left, expected_left)
@@ -307,9 +303,9 @@ class TuplesClassConstructorTests(ConstructorTests):
         params=[
             ([3, 14, 15, 92, 653], np.int64),
             (np.arange(10, dtype="int64"), np.int64),
-            (Int64Index(range(-10, 11)), np.int64),
-            (UInt64Index(range(10, 31)), np.int64),
-            (Float64Index(np.arange(20, 30, 0.5)), np.float64),
+            (NumericIndex(range(-10, 11), dtype=np.int64), np.int64),
+            (NumericIndex(range(10, 31), dtype=np.uint64), np.int64),
+            (NumericIndex(np.arange(20, 30, 0.5), dtype=np.float64), np.float64),
             (date_range("20180101", periods=10), "<M8[ns]"),
             (
                 date_range("20180101", periods=10, tz="US/Eastern"),