Charlton's third-round match with Oxford was the first to fall foul of the weather, with the decision to call the game off brought forward after an 11am inspection on Saturday had initially been planned.
Bournemouth's clash with Burton has also been called off after a late pitch inspection on Saturday revealed the surface was unplayable.
Crawley's second-round clash with Bristol Rovers has also been postponed.
Match referee Andy Davies inspected the pitch and decided the Broadfield Stadium pitch was waterlogged and unplayable.
The initial game between the two sides on 7 December had to be abandoned with the score at 0-0, also due to a waterlogged pitch.
The teams will try again on Wednesday, with Birmingham awaiting the winners of the tie in the third round.
"We had another deluge last night and parts of the pitch, particularly on the West Stand side, are under water," Chief Executive Michael Dunford told Crawley's official website.
"Taking into account the forecast for more rain tomorrow we have made an early decision to call the game off.
"The forecast for the early part of next week is not encouraging which is why we have delayed re-staging the game until Wednesday to give us the best chance of playing it then."
Motherwell's Scottish Premiership fixture against Inverness at Fir Park has also been postponed due to a waterlogged pitch.
And Portsmouth's Sky Bet League Two match against Accrington Stanley on Saturday has also been postponed due to a waterlogged pitch at Fratton Park, as well as Cheltenham's home date with Chesterfield.
Meanwhile, Woking's Skrill Premier game with Hereford has also been called off.