The Argentine defender limped off in the second half of Sunday's 3-0 Premier League win over West Ham at Old Trafford after hurting his knee during a tussle with Vladimir Coufal.
Martinez appeared to jar the knee after Coufal accidentally landed on it as he tried to stop his opponent from shielding the ball out of play, immediately pointing to the United bench in pain as he was aided by concerned team-mates.
The World Cup winner seemed to make a swift recovery though and was quickly back on his feet, sent back into the fray after brief treatment on the sidelines before going down again a few minutes later and being replaced by Raphael Varane.
Martinez had been making only his second start since September against West Ham having spent four months out with an ongoing foot injury before returning as a substitute in the 2-2 draw with Tottenham last month and also coming on in the FA Cup win at Newport, withdrawn late in the dramatic 4-3 win at Wolves on Thursday as a precaution.
The 26-year-old also missed the last several weeks of last season following the first of two surgeries on that long-standing metatarsal issue.
"It seems bad," Ten Hag admitted afterwards on Martinez's latest injury, per BBC Sport. "We have to wait, make the right diagnosis in the coming days and then we will see. Hopefully it is not too bad, we can only pray.
"He worked so hard to return and now after two games it looks like he has to sit some games out again."
Quizzed further on Martinez at his post-West Ham press conference, Ten Hag said: "I can't say (what the situation is) but it doesn't look good, so there's a big concern.
"But we have to wait for what is the diagnosis and then we can tell you more.
"Of course we do everything to get the right diagnosis and see what the damage is.
"He is very sad, very disappointed. We are all. We feel really with him.
"First of all, it's a personal disaster when it's really bad but let's wait for what it is. But also for the team it's really bad because he definitely brings us a lot."