Davies sustained the injury when twisting awkwardly during Tuesday night's 1-0 win over Peterborough in the Championship.
The setback comes just days after the 25-year-old had agreed a new contract with the Reebok Stadium club until 2017.
The former Wolves man recently returned from a shoulder injury that had kept him out for seven weeks.
Bolton manager Dougie Freedman said: "It's a blow for Mark, but he'll come back stronger.
"I believe Chris Eagles can now step up and deliver in that role."