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.

Howard, who was the president of the Screen Actors Guild - American Federation of Television and Radio Artists (SAG-AFTRA), died at his home near Los Angeles on Wednesday.
He was best known for the 1970s high school basketball series The White Shadow, in which he played the coach.
SAG-AFTRA acting president Gabrielle Carteris said he was "inspirational" and "a light that never dimmed".
A spokesman for the union added that Howard left "a legacy of service, commitment and superlative success".
"He was an extraordinary actor, a Tony and Emmy Award winner, whose career spanned Broadway, motion pictures and television," he said.
Stars of TV and film took to social media to pay tribute to Howard, who began his acting career on Broadway in 1968 after touring Europe and recording two albums with his college choral group, The Zumbyes.
Mindy Kaling, who worked with Howard on The Office, tweeted he was "a great guy",  while Terminator 2 star Robert Patrick wrote "glad I worked with 'Class'".
Rob Lowe, who starred alongside Howard in The West Wing, tweeted he would "always remember" working with him on one of his "favourite scenes ever" from the show.
George Clooney shared a memory with Deadline about meeting Howard while auditioning as a young actor.
"I didn't get that audition, but I did get the chance to work with him years later. It was an honour," he said.
"Today, his obituary read that he was six foot six, but he was so much taller than that."
Born in California on 24 March 1944, Howard first came to prominence on stage, winning a Tony Award for his role in Child's Play on Broadway in 1970.
He made his Hollywood debut in the same year, opposite Liza Minnelli in the drama Tell Me That You Love Me, Junie Moon, and would go on to star in a wide variety of films, including 1994 thriller Clear and Present Danger and 2005 comedy In Her Shoes.
However, the SAG-AFTRA spokesman said it was as Coach Reeves in the "groundbreaking" series The White Shadow he would be best remembered, adding that years after the show ended in 1981, Howard was "frequently recognised on the street by fans who greeted him with a handshake and a 'Hey, Coach'".
Howard won two Daytime Emmys for his work on television and starred in a range of shows, including Dynasty, The Colbys, Melrose Place and Crossing Jordan. He also made guest appearances on Curb Your Enthusiasm, Murder She Wrote, The Golden Girls and Law and Order: Special Victims Unit.
He was elected as the Screen Actors Guild's president in 2009 and later helped it merge with the American Federation of Television and Radio Artists to form a new 160,000-member union.
In 2011, he said in a letter to members that serving them as president was "the most important thing I have ever done".
He is survived by his wife of 25 years, Linda Fetters Howard, and three adult stepchildren from a previous marriage.
Saracens hooker Schalk Brits has been banned for three weeks after admitting a charge of striking an opponent.
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Veteran TV and film actor Ken Howard has died at the age of 71.