The 30-year-old, who has played just once this season in the Capital One Cup against Doncaster Rovers, suffered the injury in a training ground match and faces a lengthy lay-off.
A statement on the club website read: "Ross has undergone a successful operation on the injury and has already started his rehabilitation programme for what is set to be a long-term absence. Everybody at Leeds United wishes Ross all the best in his rehab and for a speedy recovery."