The Rams were leading 1-0 through Richard Keogh's header but, with the rain teeming down and surface water building up, the match was called off because of concerns for player safety.
Referee Trevor Kettle initially took the players off as a temporary measure.
But the conditions worsened and the game was abandoned soon after.
Keogh had put the Championship side ahead, heading home from Jacob Butterfield's corner, while Johnny Russell almost made it 2-0 but was denied by a fine save by keeper James McKeown.
The EFL Cup match between Grimsby Town and Derby County at Blundell Park was abandoned after 19 minutes because of heavy rain in north east Lincolnshire.