The 19-year-old won only five games on Monday in her first-round singles match against former world number one Caroline Wozniacki but had been due to compete in the doubles with American Lisa Raymond.
The pair reached the final of the WTA event in Miami in March but Robson was advised by a doctor not to play on at Roland Garros after experiencing lower back pain.
The teenager will head home to London where she will begin preparations for the grass-court season provided doctors there deem the problem is not serious.
Robson's next event is scheduled to be the AEGON Classic in Birmingham, which begins a week on Monday, before she completes her preparations for Wimbledon at Eastbourne.
Robson's withdrawal will be a big disappointment for Raymond, the winner of 11 grand slam doubles titles, who had played women's doubles in every slam since the French Open in 1995.