The defending champions overcame a red card to the All Blacks first-five to beat the Waratahs 38-28 in their Super Rugby clash in Wellington.
The World Rugby player of the year scored a try, but was also judged to have deliberately knocked the ball down twice in the match.
He was sent off in the 60th minute after receiving his second yellow card for the same offence.
The Hurricanes coach Chris Boyd hopes the red card is all that Barrett will cop.
"I don't believe that it means an automatic suspension. That's what my understanding is currently," he said after the match.
A Sanzaar press release said Barrett's case would be reviewed by the foul play committee via video conference at 9pm on Sunday (NZ time) but made no reference to of an automatic suspension.
"All Sanzaar disciplinary matters are in the first instance referred to the Foul Play Review Committee to provide the option of expediting the judicial process," the release said.
"For a matter to be dispensed with at this hearing, the person appearing must plead guilty and accept the penalty offered by the Foul Play Review Committee."
The Hurricanes raced out to a 33-7 half-time lead on the back of some sublime rugby but produced an error ridden second half as Waratahs surged back into the game to deny the hosts a bonus-point.