The 27-year-old has struggled with the problem in recent weeks and was also forced to pull out of the Monte Carlo Masters last month.
Raonic has never made it past the quarter-finals at Roland Garros, but did reach the final of Wimbledon in 2016, losing to Andy Murray.
"It is with a heavy heart that I am withdrawing from Roland Garros," Raonic said in a statement on Twitter.
"I know I need to continue working hard to put myself in the best position when I step out on the court. Thank you all for your support and see you soon on the grass."
Raonic is next due to play at the Fever-Tree Championship at Queen's, which begins on June 18.