diff --git a/numba/np/arraymath.py b/numba/np/arraymath.py
index 33460a32dda..d6d3a70b10d 100644
--- a/numba/np/arraymath.py
+++ b/numba/np/arraymath.py
@@ -1590,13 +1590,16 @@ def np_median(a):
     if not isinstance(a, types.Array):
         return
 
+    is_datetime = as_dtype(a.dtype).char in 'mM'
+
     def median_impl(a):
         # np.median() works on the flattened array, and we need a temporary
         # workspace anyway
         temp_arry = a.flatten()
         n = temp_arry.shape[0]
+        if not is_datetime and n == 0:
+            return np.nan
         return _median_inner(temp_arry, n)
-
     return median_impl
 
 
diff --git a/numba/tests/test_array_reductions.py b/numba/tests/test_array_reductions.py
index d1ca334c2d5..36b8445693e 100644
--- a/numba/tests/test_array_reductions.py
+++ b/numba/tests/test_array_reductions.py
@@ -307,6 +307,10 @@ def check(arr):
             got = cfunc(arr)
             self.assertPreciseEqual(got, expected)
 
+        # check for empty array
+        a = np.array([])
+        check(a)
+
         # Odd sizes
         def check_odd(a):
             check(a)