The 29-year-old suffered the injury during his team's 4-1 win over Nuremberg last night.
Andreasen, who had a spell in the Premier League with Fulham, has been blighted by injuries since his return to the Bundesliga in 2009, making just 22 league appearances.
"I suspected that something was damaged in my knee. The diagnosis came as no surprise to me," said the Dane.
"Certainly this is a bitter blow, but I look ahead and am convinced I can come back yet again."
The midfielder suffered the injury when his studs caught in the turf.