The 26-year-old Hungarian international suffered the problem while training with the Championship club on Monday.
Bogdan wrote on his official Facebook page: "I was unlucky because I got injured yesterday during training.
"My collateral knee ligament got torn partially. Fortunately I don't need surgery so I'm to miss 6-10 weeks."
Bolton, who are currently in 21st place in the Championship table, return to action on Saturday when they host Ipswich Town.