The loss of Bouzid for several weeks comes on top of Jim Jefferies' declaration that he will not play Jose Goncalves unless the centre-back accepts a new contract offer.
"I was disappointed to pick up the injury in the cup tie as it was such a big game for us but to be honest it is not as bad as I first thought," Bouzid told Hearts News.
"I have spoken to the doctors who have told me that I could be back training in two weeks, which is good news.
"After that it is a case of building things up and getting back into the team, maybe even a week after that.
"I don't think I will be out for too long and that is good as we have a new manager now and everyone wants to try to impress him.
"I want to get back as quickly as possible as we have a lot of important matches coming up which I want to be involved in."
Meanwhile, Jefferies will not rush back Calum Elliot, who has been missing for two months after suffering a reaction on his comeback from knee surgery.
The 22-year-old striker, who underwent the operation in August, has only made three substitute appearances this season.
"Calum is just back into training," Jefferies said. "He will step things up and see how it goes but we have to be very careful with him.
"Once he's fully fit, though, he gives us another option up front, which will be good."
Source: Team Talk