diff --git a/pandas/formats/format.py b/pandas/formats/format.py
index 4740dd25c419d..e5089983ac8f7 100644
--- a/pandas/formats/format.py
+++ b/pandas/formats/format.py
@@ -2586,6 +2586,9 @@ def __call__(self, num):
         if decimal.Decimal.is_nan(dnum):
             return 'NaN'
 
+        if decimal.Decimal.is_infinite(dnum):
+            return 'inf'
+
         sign = 1
 
         if dnum < 0:  # pragma: no cover
diff --git a/pandas/tests/formats/test_format.py b/pandas/tests/formats/test_format.py
index ba7ad55a081cd..58e9b30e7f624 100644
--- a/pandas/tests/formats/test_format.py
+++ b/pandas/tests/formats/test_format.py
@@ -4047,6 +4047,14 @@ def test_nan(self):
         self.assertTrue('NaN' in result)
         self.reset_display_options()
 
+    def test_inf(self):
+        # Issue #11981
+
+        formatter = fmt.EngFormatter(accuracy=1, use_eng_prefix=True)
+        result = formatter(np.inf)
+        self.assertEqual(result, u('inf'))
+
+
 def _three_digit_exp():
     return '%.4g' % 1.7e8 == '1.7e+008'