diff --git a/nibabel/tests/test_utils.py b/nibabel/tests/test_utils.py
index 1810722b55..83122bbe95 100644
--- a/nibabel/tests/test_utils.py
+++ b/nibabel/tests/test_utils.py
@@ -1227,3 +1227,21 @@ def assert_rt(data,
                       slope = slope,
                       post_clips = post_clips,
                       nan_fill = nan_fill)
+
+
+def test_array_from_file_overflow():
+    # Test for int overflow in size calculation in array_from_file
+    shape = (1500,) * 6
+    class NoStringIO:  # Null file-like for forcing error
+        def seek(self, n_bytes):
+            pass
+        def read(self, n_bytes):
+            return b''
+    try:
+        array_from_file(shape, np.int8, NoStringIO())
+    except IOError as err:
+        message = str(err)
+    assert_equal(message,
+                 'Expected {0} bytes, got {1} bytes from {2}\n'
+                 ' - could the file be damaged?'.format(
+                     11390625000000000000, 0, 'object'))
diff --git a/nibabel/volumeutils.py b/nibabel/volumeutils.py
index d43c43f4cc..ce2e0cd6ac 100644
--- a/nibabel/volumeutils.py
+++ b/nibabel/volumeutils.py
@@ -14,6 +14,8 @@
 import gzip
 import bz2
 from os.path import exists, splitext
+from operator import mul
+from functools import reduce
 
 import numpy as np
 
@@ -504,7 +506,8 @@ def array_from_file(shape, in_dtype, infile, offset=0, order='F', mmap=True):
             pass
     if len(shape) == 0:
         return np.array([])
-    n_bytes = int(np.prod(shape) * in_dtype.itemsize)
+    # Use reduce and mul to work around numpy integer overflow
+    n_bytes = reduce(mul, shape) * in_dtype.itemsize
     if n_bytes == 0:
         return np.array([])
     # Read data from file