As revealed by Standard Sport earlier on Sunday, the goalkeeper missed the trip to Old Trafford and was replaced in the travelling party by 17-year-old Jamie Cumming.
Courtois misses a Premier League game for the first time this season, six days before a FA Cup semi-final date with Tottenham at Wembley. Conte expressed doubt over his recovery time.
"During the week he had an injury in his ankle and he didn't recover for this game," Conte told Sky Sports.
"I hope [he misses] only this game."
Conte appeared to also confirm Courtois suffered the injury playing basketball during a commercial shoot.
When questioned, he replied: "It's not important to understand the way he had this the injury.
"Courtois for sure is one of the best goalkeepers in the world, but we trust a lot in Begovic and I'm sure he'll play a great game."
Chelsea face United 24 hours after Tottenham again closed the gap on the Premier League leaders to four points, having successful restored their seven-point advantage last weekend.
Sunday's Old Trafford game is arguably Chelsea's toughest in the title run-in and will have been boosted by Jose Mourinho's decision to drop a "very tired" Zlatan Ibrahimovic to the substitutes' bench.