The 31-year-old Irishman, affected by the problem for most of the season, last appeared for the Bantams at the end of December. He will have a piece of floating bone removed and will be sidelined for six weeks.
City manager Peter Taylor said: "He turned his ankle over at the training ground because of the hard conditions.
"It wasn't from a tackle, but he's hurt it again and it looks likely he'll have to get it done.
"He's going to be out for up to six weeks unfortunately, which is another blow for us."