“I will only take part in Roland Garros if I am 100 per cent fit,” said Sinner at a press conference held in Rome.
“I don’t want to go into details (of the injury), we thought initially that it wasn’t anything serious but the scans showed that there was something that wasn’t right.
“One thing is sure, if I’ve not 100 per cent recovered I will take more time out as I do not want to lose three years of my career.
“It hurts (not playing) but making sure my body heals is the most important thing.”
Sinner, who holds a 28-2 record on the season, added that he would out of action “for a week, a week and a half”.
“My preparation for Paris won’t be optimal because I won’t have much time, but what is sure is that I will give everything in order to be in a position to play,” he said.
Sinner had been a doubt for the Italian Open which starts on Wednesday and is the last big tournament before the French Open, the second Grand Slam of the year starting on May 26.
The 22-year-old was due to face Felix Auger-Aliassime in the Madrid quarter-finals on Thursday but pulled out due to his hip issue.
Even though he is not a clay court specialist Sinner would have been one of the favourites for the tournament in Rome after a stunning start to the year.
He won the Australian Open, his first Slam title, in January and followed that up with his second Masters 1000 crown in Miami in March.
Sinner joins world No 3 Carlos Alcaraz in withdrawing from the event in the Italian capital after the Spaniard succumbed to a right forearm injury that sidelined him in Monte Carlo and Barcelona.