Flood, who made his City debut in the first ever match at the Ricoh Arena against QPR in August 2005, got the injury in an accidental collision with team-mate Matthew Bates.
Speaking to BBC Radio Tees, Middlesbrough manager and former Sky Blue Gordon Strachan said: "We're not going to see Willo for a long time, it's a bad injury. "That's a bad blow because we saw last year when he first joined us that he was a real asset."