Brits has received a three-week suspension following an International Rugby Board disciplinary hearing in Hong Kong, the International Rugby Board confirmed.
He was cited after hitting Farrell with his arm during Saturday's game between the Barbarians and British and Irish Lions at Hong Kong Stadium.
Brits was cited by IRB citing commissioner Simon Ryan, and he appeared at a hearing before IRB judicial officer Steve Lewis on Sunday.
Saturday's game was the last one Brits will play this season, and his playing schedule for next term has not yet been determined.
The ban could ultimately include part of Saracens' pre-season schedule, but at this stage he is sidelined for their opening three Premiership fixtures.
Lewis decided that Brits's offence was mid-range and warranted an entry point of five weeks, but sanction was reduced to three weeks because of "compelling mitigating factors".
A statement released after the hearing read: "The IRB's sanctions for foul play have been established on the basis that a one-week period of suspension would normally result in a player missing one match.
"Consequently, he is suspended from all rugby up to and including the third Aviva Premiership match of the 2013-14 season, unless the judicial officer confirms in writing that any pre-season match shall be considered meaningful for the purpose of regulation 17.19.11 (d), in which case such match shall be included as one of the three matches."
Referee Steve Walsh initially penalised Farrell for reacting to Brits, but then reversed his decision after consulting television replays. He also yellow-carded the Saracens forward.