Brebner was sent off by match referee Stuart Dougal following a challenge on Hearts striker Robert Sloan in an ill-tempered derby clash at Easter Road.
Dougal deemed the 25-year-old's challenge on Sloan was serious enough to warrant a sending off at the time.
However, an SFA review panel upheld an appeal made by Hibs and Brebner and the midfielder will only receive a caution for his challenge in last Sunday's 1-0 derby victory.
"In reviewing the video footage of the incident which led to the red card, the panel also took into account the views of the match referee, Stuart Dougal," an SFA spokesman said.
"He advised them that, having watched the incident again, he accepted that a yellow card would have been a more appropriate sanction."
