The centre-back has impressed for the Urban Warriors since his off-season switch from Pirates, as evidenced by his man-of-the-match award in a recent 2-2 draw with log leaders Baroka.
However, a scan after the Cape derby loss to Cape Town City on the weekend revealed Malepe has a stress fracture of his L5 vertebrae.
Ajax's head of medical Jantho Greyling explained the situation on the club's website.
"We got a bit of bad news on Monday after the derby game. We sent Tercious for a CT scan of his lower back and we found that he has a stress fracture of his L5 vertebrae. Which means that he will be out of action for a minimum of six weeks after which we will take another CT scan and see if that bone, vertebrae has healed and then slowly get him back into it.
"But, yes, he will probably be out for around six weeks which is a big blow for us because he was doing very well. It is a very unfortunate injury."
Fellow recruit Morne Nel is expected back next year afer having groin surgery on Monday, but Toriq 'Tokkie' Losper is close to returning for Stanley Menzo's side as he makes his way back from a hip problem. He has been reganing fitness in the MultiChoice Diski Challenge.
"Morne underwent surgery on Monday, the surgery went very well and he is out of hospital, he is at home recovering. But, as we all know, he will only be back in action next year," said Greyling
"The operation, though, was successful and he is recovering, hopefully he will recover as soon as possible. That said, he has a long rehab process that he first has to follow and then we will have a better idea when he will be back on the field."
He added: "Tokkie has recovered fully from the hip injury he had, he is doing very well and he has played two MDC games to get his fitness back. He also played in a friendly match this week, 70 minutes, so it is just a question of getting his match fitness back, but he is doing very well.
“Hopefully we can use him for the PSL team as soon as possible, he is getting back to his best."