The former Dons midfielder was shown a straight red card for a challenge on Aberdeen striker Stevie May, but appealed on the basis of ‘wrongful dismissal for A1 serious foul play’.
But a Fast Track Disciplinary Tribunal threw out the appeal, with the original three-match suspension being applied.
Although Jack initially won the ball in the challenge, he connected heavily with May’s ankle, with the former St Johnstone striker going off injured shortly after to be replaced by Nicky Maynard.
It was the fourth red card shown to the 25-year-old since he swapped Pittodrie for Ibrox in the summer - prior to his transfer he had been sent off three times in his career.
Two of his previous sendings-off - against Hibs and Kilmarnock - were overturned on appeal but the SFA’s decision to dismiss Jack’s appeal means the midfielder misses Rangers’ matches with Ross County, Hibs and Kilmarnock.
• An earlier version of this article stated that Jack would miss the game against St Johnstone - however, because the third match of his suspension is a result of his previous red card the third match suspension is activated two weeks after the most recent offence, meaning Jack misses the trip to Kilmarnock and not the home tie against the Saints