The 26-year-old has been an ever-present for Dougie Freedman's Trotters so far this season, starting in all 12 of their Sky Bet Championship games.
Bolton drew 1-1 with Sheffield Wednesday on Saturday and are currently 21st in the table - but have lost the services of their first-choice keeper due to an injury sustained in training on Monday.
"I was unlucky because I got injured yesterday during training", the Hungarian international posted on his official Facebook page.
"My collateral knee ligament got torn partially. Fortunately I don't need surgery so I'm to miss 6-10 weeks."
Former Preston and Leeds goalkeeper Andy Lonergan is likely to deputise in Bogdan's absence, having played twice so far in Capital One Cup ties.