The 20-year-old Swiss full-back has been told he will have to wear a protective mask when he does eventually return to action.
"Mihael's been in the gym and out running, it's just contact stuff he has to avoid so he'll be able to keep ticking over," Terrors boss Craig Levein told The Courier.
"But he won't play again for six weeks and then we'll have to sort out a mask.
"It's a pity to lose him as he's different to the other full-backs we have and generally he's done well for us. But fortunately we have a decent-sized squad."