Garbutt was sent off after 71 minutes for punching opponent James Tamou.
The Australian, 26, faced a two or three-game ban for punching, but submitted an early guilty plea and received the more lenient punishment.
The Cowboys won 38-4 to complete a 3-0 World Club Series win for the NRL.
Leeds Rhinos prop Mitch Garbutt has been suspended for two matches following his red card in Sunday's World Club Challenge defeat by North Queensland Cowboys at Headingley.