The 34-year-old South Africa international was sent off in the first half of Saturday's victory over Gloucester for a punch on Nick Wood.
Brits pleaded guilty to the charge at a Rugby Football Union disciplinary hearing on Tuesday.
He will miss matches against Sale, Northampton and London Irish and will be available to play again on 15 March.
Saracens hooker Schalk Brits has been banned for three weeks after admitting a charge of striking an opponent.