The match was scheduled to start shortly after midday in front of a sell-out 4,500 crowd, but the bad weather conditions forced umpires to hold a pitch inspection an hour prior.
With no sign of the rain relenting after the delayed start, the game was called off later in the afternoon without a ball being bowled.
The final game of the three-match series is scheduled for Sunday.
Inspired by Phil Salt's superb 89 from 46 balls, England successfully chased 197 to win Wednesday's opener by four wickets.