diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index c24c94a786068..0bc568fb122ed 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4962,14 +4962,6 @@ def _raise_scalar_data_error(cls, data):
             f"kind, {repr(data)} was passed"
         )
 
-    @final
-    @classmethod
-    def _string_data_error(cls, data):
-        raise TypeError(
-            "String dtype not supported, you may need "
-            "to explicitly cast to a numeric type"
-        )
-
     def _validate_fill_value(self, value):
         """
         Check if the value can be inserted into our array without casting,
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index 816a1752c5bf0..328e3d2f401e6 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -32,6 +32,7 @@
 )
 from pandas.core.dtypes.generic import ABCSeries
 
+from pandas.core.construction import sanitize_array
 from pandas.core.indexes.base import (
     Index,
     maybe_extract_name,
@@ -144,15 +145,17 @@ def _ensure_array(cls, data, dtype, copy: bool):
                 data = list(data)
 
             orig = data
-            data = np.asarray(data, dtype=dtype)
+            if isinstance(data, (list, tuple)):
+                if len(data):
+                    data = sanitize_array(data, index=None)
+                else:
+                    data = np.array([], dtype=np.int64)
+
             if dtype is None and data.dtype.kind == "f":
                 if cls is UInt64Index and (data >= 0).all():
                     # https://github.com/numpy/numpy/issues/19146
                     data = np.asarray(orig, dtype=np.uint64)
 
-        if issubclass(data.dtype.type, str):
-            cls._string_data_error(data)
-
         dtype = cls._ensure_dtype(dtype)
 
         if copy or not is_dtype_equal(data.dtype, dtype):
@@ -198,7 +201,8 @@ def _ensure_dtype(cls, dtype: Dtype | None) -> np.dtype | None:
             return cls._default_dtype
 
         dtype = pandas_dtype(dtype)
-        assert isinstance(dtype, np.dtype)
+        if not isinstance(dtype, np.dtype):
+            raise TypeError(f"{dtype} not a numpy type")
 
         if cls._is_backward_compat_public_numeric_index:
             # dtype for NumericIndex
diff --git a/pandas/tests/indexes/numeric/test_numeric.py b/pandas/tests/indexes/numeric/test_numeric.py
index 8901ef7cb3e33..c06fce4811f12 100644
--- a/pandas/tests/indexes/numeric/test_numeric.py
+++ b/pandas/tests/indexes/numeric/test_numeric.py
@@ -64,6 +64,10 @@ def check_coerce(self, a, b, is_float_index=True):
         else:
             self.check_is_index(b)
 
+    def test_constructor_from_list_no_dtype(self):
+        index = self._index_cls([1.5, 2.5, 3.5])
+        assert index.dtype == np.float64
+
     def test_constructor(self, dtype):
         index_cls = self._index_cls
 
@@ -115,17 +119,10 @@ def test_constructor_invalid(self):
         with pytest.raises(TypeError, match=msg):
             index_cls(0.0)
 
-        # 2021-02-1 we get ValueError in numpy 1.20, but not on all builds
-        msg = "|".join(
-            [
-                "String dtype not supported, you may need to explicitly cast ",
-                "could not convert string to float: 'a'",
-            ]
-        )
-        with pytest.raises((TypeError, ValueError), match=msg):
+        msg = f"data is not compatible with {index_cls.__name__}"
+        with pytest.raises(ValueError, match=msg):
             index_cls(["a", "b", 0.0])
 
-        msg = f"data is not compatible with {index_cls.__name__}"
         with pytest.raises(ValueError, match=msg):
             index_cls([Timestamp("20130101")])
 
@@ -327,18 +324,16 @@ def test_identical(self, simple_index, dtype):
         assert not index.astype(dtype=object).identical(index.astype(dtype=dtype))
 
     def test_cant_or_shouldnt_cast(self):
-        msg = (
-            "String dtype not supported, "
-            "you may need to explicitly cast to a numeric type"
-        )
+        msg = f"data is not compatible with {self._index_cls.__name__}"
+
         # can't
         data = ["foo", "bar", "baz"]
-        with pytest.raises(TypeError, match=msg):
+        with pytest.raises(ValueError, match=msg):
             self._index_cls(data)
 
         # shouldn't
         data = ["0", "1", "2"]
-        with pytest.raises(TypeError, match=msg):
+        with pytest.raises(ValueError, match=msg):
             self._index_cls(data)
 
     def test_view_index(self, simple_index):
@@ -372,6 +367,10 @@ def simple_index(self, dtype):
     def index(self, request, dtype):
         return self._index_cls(request.param, dtype=dtype)
 
+    def test_constructor_from_list_no_dtype(self):
+        index = self._index_cls([1, 2, 3])
+        assert index.dtype == np.int64
+
     def test_constructor(self, dtype):
         index_cls = self._index_cls