Martinez missed the end of last season after fracturing a bone in his right foot in April. He returned to the squad in the summer but was substituted during the 3-1 defeat to Arsenal on Sep. 3 after the aggravating the problem.
"We did a proper diagnosis, in Argentina as well, but now it came out that there was a problem," Ten Hag told a news conference on Friday. "That's very sad, for him and the team, because he was not 100% fit."
Martinez was in the team which conceded 14 goals in games against Tottenham, Nottingham Forest, Arsenal, Brighton and Bayern.
"I think it was a big difference, the Licha Martinez in the last games and the Licha Martinez we have seen in the first season here," added the Dutchman.
"He will add to the team, a really strong contributor to our levels and if already one player drops a level, the team performance will be lower."
Ten Hag has spoken to Antony regularly during his time in Brazil but says he will assess the winger's mental state before deciding when to bring him back into the team.
"I've spoken to him, but that doesn't give the impression how he is, how his mental status is," said Ten Hag.
"I can't tell at this moment, first he has to be back."