Courtois sustained the blow during training and is not with the squad that will start at Old Trafford.
It means back-up keeper Asmir Begovic will start the match instead for what will be his first start in the League this season.
Begovic has only made six appearances for the Blues this term, the last of which was against Wolves in the FA Cup Fifth Round in February.
The Bosnia international wanted to join Bournemouth in a £10million deal in January having grown fed up over the lack of first team football.
However, Chelsea blocked the move after failing to find a replacement, with bids for Celtic goalie Craig Gordon rejected.
Manchester United are bound to target Begovic this afternoon and see if Chelsea's defence is rattled by Courtois' absence.
Chelsea are under pressure to get at least a draw from the encounter after Tottenham beat Bournemouth 4-0 yesterday to close the gap to Antonio Conte's side to four points.
The two London clubs are playing each other in the FA Cup semi-final at Wembley on Saturday.
It is believed Courtois' injury is only minor, and the goalkeeper has not been ruled out of that game as of yet.