The Rangers goalkeeper landed on Motherwell captain Peter Hartley after a coming together of players following a corner during the second half of the 3-3 draw between the two clubs at the weekend.
The incident angered both benches, however it is understood that the goalkeeper will not be punished for his actions.
The SFA compliance officer is understood to have decided "there is no case to answer".
August 27, 2018
McGregor re-joined Rangers in the summer on a two-year deal and had conceded just three goals in eight appearances before Sunday's game.