diff --git a/pandas/core/series.py b/pandas/core/series.py
index 3a7a7d0f49b66..3439aeb79e174 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -3180,14 +3180,15 @@ def interpolate(self, method='linear'):
         invalid = isnull(values)
         valid = -invalid
 
-        firstIndex = valid.argmax()
-        valid = valid[firstIndex:]
-        invalid = invalid[firstIndex:]
-        inds = inds[firstIndex:]
-
         result = values.copy()
-        result[firstIndex:][invalid] = np.interp(inds[invalid], inds[valid],
-                                                 values[firstIndex:][valid])
+        if valid.any():
+            firstIndex = valid.argmax()
+            valid = valid[firstIndex:]
+            invalid = invalid[firstIndex:]
+            inds = inds[firstIndex:]
+
+            result[firstIndex:][invalid] = np.interp(
+                inds[invalid], inds[valid], values[firstIndex:][valid])
 
         return Series(result, index=self.index, name=self.name)
 
diff --git a/pandas/tests/test_series.py b/pandas/tests/test_series.py
index e1589b9499757..58ca34b73b6a0 100644
--- a/pandas/tests/test_series.py
+++ b/pandas/tests/test_series.py
@@ -4063,6 +4063,13 @@ def test_interpolate(self):
         # try time interpolation on a non-TimeSeries
         self.assertRaises(Exception, self.series.interpolate, method='time')
 
+    def test_interpolate_corners(self):
+        s = Series([np.nan, np.nan])
+        assert_series_equal(s.interpolate(), s)
+
+        s = Series([]).interpolate()
+        assert_series_equal(s.interpolate(), s)
+
     def test_interpolate_index_values(self):
         s = Series(np.nan, index=np.sort(np.random.rand(30)))
         s[::3] = np.random.randn(10)