Milnes was forced off against Eastwood Town on New Year’s Day after sustaining ankle ligament damage.
The 20-year-old is undergoing treatment and rehabilitation with sports therapist Katie Cooper and could be back by the end of January.
Cooper told bufc.co.uk: “Ben’s injury is not quite as bad as first feared.
“He has suffered minor medial ankle ligament damage and is already entering the rehabilitation stage of his comeback.
“We hope Ben will not be sidelined for more than two to three weeks.”