Bayern Munich's Austrian international midfielder David Alaba has undergone successful knee surgery and could return to full training by early January, the Bundesliga champions announced on Friday.

The 22-year-old sustained an injury to his meniscus during Wednesday's 2-0 Champions League victory over Roma which guaranteed Bayern top spot in their group and qualification for the knockout phase next year.

"It's a bitter moment for me because everything was going well both for the club and myself," Alaba, who set up the opening goal for French winger Franck Ribery, said on the eve of his operation.

"With the help of the medical staff, I hope to be back on the pitch as soon as possible."

Alaba has played in all of Bayern's 17 matches this season before injury derailed his season at the Allianz Arena in midweek.