The all-action Scotsman was not able to finish their 1-1 draw against Burnley in the Premier League.
McTominay, who has netted vital goals from midfield, faces a race against time to make the FA Cup final.
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Speaking with club media, Ten Hag said: "We have to assess this, to set the diagnosis.
"I don't know in this moment to return (against Crystal Palace next month), I think it's a little bit too quick turnaround."
"I don't know," he added to TV interviewers.
"You have seen he has a problem. We have to diagnose this and see what it is."