The 26-year-old let his tempers get the better of him towards the end of the clash at Headingley, landing a hefty punch to Tamou's face before both players were sin-binned.
A belter of a punch from Leeds' Mitch Garbutt floors James Tamou during the World Club Challenge. pic.twitter.com/mmd20c0I8m— Newshub Sport (@NewshubSport) February 21, 2016
The Australian admitted the "grade C" punching offence and was given a two-game suspension for his "early guilty plea", the RFL confirmed.
The ban means that Garbutt will miss the Super League champions' games against Catalans Dragons and Huddersfield Giants in the next fortnight.