The Red Devils experienced a frustrating afternoon at Old Trafford after Zeki Amdouni scored an 87th-minute penalty to cancel out Antony's opener.
Man United's difficult outing was compounded in stoppage time when McTominay limped off due to an apparent knee injury.
McTominay was brought on as a substitute for Kobbie Mainoo just after the hour mark, but he was unable to see out the contest and was subsequently replaced by Mason Mount in the second minute of stoppage time.
The Scotland international looked to be in agony as he punched the ground while the Man United physios tended to him.
McTominay set to be assessed
Man United now face an anxious wait to learn whether McTominay will be available for any of their final four Premier League games as well as next month's FA Cup final against Manchester City.
When asked about McTominay after the draw with Burnley, Erik ten Hag told reporters: "Yeah, we have to assess with the doctors, the diagnosis I don't know at this moment."
McTominay has been a regular fixture in the Man United side this season, scoring 10 goals and providing three assists in 39 appearances.
Scotland wait to learn extent of McTominay's injury
In addition to Ten Hag, Scotland boss Steve Clarke also faces a nervous wait to find out the extent of McTominay's injury ahead of Euro 2024.
The midfielder was a key figure in Scotland's qualifying campaign, scoring eight goals in as many games to seal his country's place in Germany.
Scotland are already without Bologna midfielder Lewis Ferguson, who recently sustained an anterior cruciate ligament injury.
There are also concerns surrounding the availability of Aaron Hickey, Nathan Patterson, Stuart Armstrong and Kieran Tierney.
Scotland are due to begin their 2024 campaign against tournament hosts Germany on June 14, before they round off the group stage with games against Switzerland and Hungary.