The match has been scheduled for Sunday rather than Saturday as Chelsea face a trip to Russia to take on Rubin Kazan in the Europa League on April 11, and the FA needed to make a decision before the Blues' quarter-final replay with United on April 1.
Championship side Millwall will therefore take on Wigan, who have reached the last four for the first time, in the other semi-final at Wembley at 5.15pm on Saturday April 13.
Millwall and Manchester City have been allocated the west end of the stadium and will receive 31,514 tickets.
Wigan and the other semi-finalists will be given 31,863 tickets.
The winning clubs in both games earn £900,000 from the FA Cup Prize Fund, with the runners-up collecting £450,000.