Both players would have been in line to start for Erik ten Hag against Manchester City in the FA Cup final, but are now serious doubts with the Wembley showpiece just nine days away on June 3.
The Brazil international, who held his face as he was carried off, looked in distress as he left the field in the 29th minute, and Ten Hag consoled him with a pat on the stomach before he was taken to the locker rooms.
It was not immediately clear what part of the body Antony hurt, but he was in pain after a challenge from Chelsea defender Trevoh Chalobah. Antony was replaced by Marcus Rashford, who was just returning to the team from an injury of his own.
Ten Hag said afterwards: "Everyone has seen he [Antony] came off. I can tell you that it's serious, but we have to wait a minimum of 24 hours and then we know probably more about the status of his injury."
Victory over Chelsea secured a top-four finish for United ahead of the final game of the season against Fulham at Old Trafford on Sunday. It means Ten Hag's team will return to the Champions League next season, but the Dutchman insists the club should be setting their sights higher.
"I think in this league, that's a good base to be in the top four, but we want to compete for the title," Ten Hag said. "But it has to be realistic and you can first say when you have your squad in the end of the transfer window and also the winter transfer window what you can do. The squad is there and you can make a statement about if it's realistic or not.
"Now we are far away, so we have a lot of work to do. We've made progress with this team, with this squad but we need better players if we want to compete for the highest."