The Norway international could miss up to eight Premier League matches during that time, as well as Fulham's FA Cup third round clash in early January.
Hangeland has not featured since their 4-1 victory over Crystal Palace in October, and he was replaced at half-time during the clash at Selhurst Park.
The extent of the 33-year-old's injury was revealed on Friday after he underwent a successful operation to rectify a nerve problem.
"The club can confirm that Brede Hangeland underwent surgery on Thursday evening to address a nerve problem in his right leg, from which he has been suffering," a statement from the club said.
"The procedure went well and the musculature appears healthy following the operation.
"Brede will begin his rehabilitation straight away with an estimated return time of six weeks."
Fulham have not picked up a single point since Hangeland's injury and replaced manager Martin Jol with Rene Meulensteen last weekend in attempt to end a run of seven straight defeats.