The veteran centre-half suffered ligament damage in training last week.
Hurzeler told Brighton's website: "Adam sustained a ligaments injury to his knee during training last week and he has to operate over the coming weeks.
"Unfortunately, it was a case of pure accident. It's a hard blow for Adam – especially after he returned to top form up to the new season. It is also a blow to us as he has been an important player for the team. He is a great personality and a leader in the squad.
"We will work closely with him in the coming months to ensure that he gets the best possible treatment and rehabilitation so that he can return in full shape as soon as possible. It's still too early to say something exactly about how long he wants to be out, but it's fair to say he's going to miss a big part of the season."