The 57-cap All Black will miss the Hurricanes match against New Zealand rivals the Crusaders this weekend as a result of the suspension.
Nonu was shown the yellow card for a professional foul after 29 minutes of Friday's match after referee Stuart Dickinson had warned the Hurricanes about infringements at the breakdown.
His second yellow, and consequent red card, came when he shoulder-charged Highlanders' scrumhalf Jimmy Cowan and caught his New Zealand team-mate in the neck after 50 minutes. He was later cited for the dangerous tackle.
"SANZAR judicial officer Nigel Hampton QC upheld the citing on the basis that Nonu did not use his arms in the tackle and the first impact was with his shoulder into Cowan's neck," read a news release from the competition's organisers.
Playing the last 30 minutes against 14 men, the Highlanders went on to win the opening match of the Super Rugby season 14-9.