"There was sufficient evidence to support that contact had been made with the right eye and bridge of the nose,'' he ruled.
Byrnes was left disappointed by the ruling and Rebels officials declared their intention to appeal on Sunday night.
''(The) Rebels share Byrnes' disappointment with this finding and will fully support him throughout the appeal process,'' the franchise said in a statement.
"The club would also like to make it clear that despite media reports, there is no suggestion that Byrnes engaged in any eye gouging.
"We believe any contact made was absolutely accidental and without intent.''
The entry point of Byrnes' offence is 12 weeks but two weeks credit was given for his otherwise unblemished record - meaning he is set to be sidelined until the Rebels meet the Western Force on May 20.
It immediately leaves the Rebels' big-man stocks light on in depth for Saturday night's clash with defending champions Queensland, who boast Wallabies locks James Horwill and Rob Simmons and two other lineout options in Radike Samo and Jake Schatz.
The second-placed Reds are coming off a 35-20 victory over the Western Force at Suncorp Stadium to be the only Australian team to have won their first two matches.
But coach Ewen McKenzie said he'll be addressing his defence after David Pocock and James Stannard strolled through for two soft tries within five minutes to come back from 26-6 down.
Force coach Richard Graham continued to lament a host of early-season breakdown penalties which has led to conservative tactics.
"There's certainly some confusion in that area of the game and a lack of consistency,'' he said.
"You have to play at the right end of the field at the moment until you get an appreciation for it.''
- AAP