The game - originally scheduled for Sunday 20 December but postponed due to a waterlogged pitch - will now take place on Sunday 28 February in a 14:00 (UK) kick-off at Damson Park.
The pair have met on 20 occasions in all competitions since 2014, including the 2017 FA Cup and 2016 Continental Cup Finals, with City victorious in 14.
Gareth Taylor's side are unbeaten in our last eight league games, winning our last five.
Birmingham have won three of their last seven but played only two games in January due to postponements.
The game will be shown live on the FA Player.