diff --git a/numpy/core/getlimits.py b/numpy/core/getlimits.py
index da9e1d7f311c..13414c2a64d6 100644
--- a/numpy/core/getlimits.py
+++ b/numpy/core/getlimits.py
@@ -482,9 +482,12 @@ class finfo:
     _finfo_cache = {}
 
     def __new__(cls, dtype):
-        obj = cls._finfo_cache.get(dtype)  # most common path
-        if obj is not None:
-            return obj
+        try:
+            obj = cls._finfo_cache.get(dtype)  # most common path
+            if obj is not None:
+                return obj
+        except TypeError:
+            pass
 
         if dtype is None:
             # Deprecated in NumPy 1.25, 2023-01-16
diff --git a/numpy/core/tests/test_getlimits.py b/numpy/core/tests/test_getlimits.py
index 63217c38c098..f646e2bd7980 100644
--- a/numpy/core/tests/test_getlimits.py
+++ b/numpy/core/tests/test_getlimits.py
@@ -73,6 +73,15 @@ def test_regression_gh23108(self):
         f2 = np.finfo(np.float64(1.0))
         assert f1 != f2
 
+    def test_regression_gh23867(self):
+        class NonHashableWithDtype:
+            __hash__ = None
+            dtype = np.dtype('float32')
+  
+        x = NonHashableWithDtype()
+        assert np.finfo(x) == np.finfo(x.dtype)
+        
+
 class TestIinfo:
     def test_basic(self):
         dts = list(zip(['i1', 'i2', 'i4', 'i8',