The Limpopo-based club are currently third on the log table with seven points from four matches, with only one point separating them from joint leaders JDR Stars and Pretoria University.
Last season Medic impressed many when he took TTM to the promotion playoffs after only arriving in February.
A statement on the club's social media platforms says the former Orlando Pirates assistant coach was suspended due to conflicts between the team.
But according to a source inside the camp, the coach was suspended for something that happened last season when the club contravened the NSL handbook rules against TS Sporting.
TTM failed to field three under-23 players on 20 April 2019. The club was fined R30 000 for the incident, with 50 percent suspended for 12 months.
"The coach is being punished because of that game, because of that case," a reliable source tells snl24.com/kickoff.
Meanwhile, club president Lawrence Mulaudzi is being accused of constantly interfering with the coach's job.
"Sometimes he [Mulaudzi] comes to the dressing room and changes the line-up and says bad things about the coach in front of the players. He suspended him in front of the players," the source adds.
"Definitely I don't think they will continue with Medic. It will not be possible for both parties to work together again."
Medic's assistant Phuthi Mohafe is currently in charge of the team.
After nine combined calls both Mulaudzi and CEO Sello Chokoe could not be reached for comment.