United manager Simon Grayson revealed that Parker is facing "a few months" on the sidelines as the defender recovers from the latest problem to trouble him.
Parker underwent a scan soon after limping from the field during the second half of Leeds' 4-1 defeat of MK Dons but he was sent for a second inspection ahead of the final game of the season amid fears that the injury might be more than a simple calf strain.
His appearance against MK Dons was only his second start of the term, apparently ending a long run of fitness concerns which began with a hamstring strain on the first day of the season and continued with hip surgery at the start of October.