Antony was introduced for Marcus Rashford in the 73rd minute of the affair in Istanbul, but he was unable to complete the match, with Amad Diallo replacing the Brazilian in the final exchanges.
The ex-Ajax attacker left the stadium in a protective boot, and Man United head coach Erik ten Hag has said that he will now need to be assessed before the extent of the damage can be revealed.
"It's really unlucky for him," Ten Hag told MUTV after the 1-1 draw with Fenerbahce. "I feel real compassion for him, when he worked so hard in training.
"His training performances are that good that he deserved to come on. When you have to come off so quickly, that is really sad to see. Hopefully, it's not too bad, we have to wait 24 hours for what the assessment is."
Man United's Antony leaves stadium in a protective boot
Christian Eriksen sent Man United ahead against Fenerbahce, but Youssef En-Nesyri levelled the scores in the second period, with the Red Devils still waiting for their first European win of the campaign.
"It was a good game, two good teams, both went for the win. We want to win and when you are 1-0 up in a tough away game, after a first half where you have control and we had some good chances to make a second [goal], then you concede a goal like we did, that feels bad," Ten Hag added.
"The first ball was played in our block, that cannot happen. Then one cross has come in and then a goal, that shouldn't happen.
"We should have won this game but, in the end, we know that it's a tough atmosphere here, so we take a point. So from two tough away games [also against FC Porto], we take two points and now we have two games at Old Trafford [in the Europa League]. We have to win if we want to progress in Europe."
Who else is currently injured for Man United?
Man United were without the services of a number of players against Fenerbahce, including Bruno Fernandes, with the Portugal international serving a one-game suspension on Thursday night.
Meanwhile, Tyrell Malacia, Leny Yoro, Luke Shaw, Kobbie Mainoo, Mason Mount, Jonny Evans, Toby Collyer and Harry Maguire were all missing for the European fixture due to injury.,
Man United will be aiming to make it successive wins in the Premier League when they head to West Ham United on Sunday afternoon, before switching their attention to the EFL Cup and a home fixture with Leicester City.