"Naturally I am very disappointed," said Olic, who last season scored 19 goals in 41 games in all competitions.
"I expected to continue the good run of last season and had high hopes this season," he said in a brief statement.
Bayern said Olic would fly to the United States where he would most likely have surgery on his left knee this week.
Olic suffered meniscus damage playing for Croatia in August.
His absence over the next six months is another huge blow to Bayern who are already without long-time injured wingers Arjen Robben and Franck Ribery, as well as key striker Miroslav Klose.
Bayern are seventh in the Bundesliga. The German champions face Romania's CFR Cluj in the Champions League on Wednesday knowing that a point would put them through to the last 16 with two matches to spare.
They are missing nine players through injury for the game against Cluj, including defender Diego Contento and captain Mark van Bommel, while defender Holger Badstuber is also doubtful after picking up an injury during the warm-up before their league win against Freiburg on Friday.
"It is still unclear whether Badstuber will travel with the team to Romania," Bayern said.
