Cooper was yellow-carded and placed on report for tackling his Australia team-mate 'above the shoulder line' in the 63rd minute of this weekend's clash at Suncorp Stadium, which the Reds won 32-16 to seal a play-off spot.
Following a marathon five-hour hearing via video link, SANZAR judicial officer Paul Tully delivered the guilty verdict that threatens to undermine the Reds' title defence.
The decision is a major blow to the reigning champions, who won their last six regular-season games to finish top of the Australian Conference.
A disappointed Cooper immediately took to Twitter to express faith in his team-mates on Monday night, saying: "Thank you for the concern and support! Our team has worked very hard...the outcome is a week suspension. I have faith in my team and my team-mates."
Utility Ben Lucas and inside-centre Mike Harris are the front-runners to take over the fly-half spot in Cooper's absence.
If the Reds are able to defeat the Sharks this weekend, Cooper will be available for a likely semi-final showdown with New Zealand Conference winners the Chiefs in Hamilton.