Sinner sustained the injury at Madrid and pulled out of his quarter-final against Canada's Felix Auger-Aliassime last week, before the Italian decided to skip the Rome tournament which runs from May 8-19.
The 22-year-old, who claimed his maiden grand slam title in Melbourne in January, said the injury was more serious than initially suspected.
"At Roland Garros, I'll only play if I'm 100 per cent if there's any doubt we have to see," Sinner told reporters.
"Some injuries can be prevented, some can't. So far we've done a great job, last year I played a whole season without injuries and also in this season so far."
Sinner said he could prioritise his health over the year's second grand slam, which begins on May 26.
"Now I'll have a period without playing... we need to see how to work from next week onwards," Sinner added.
"Preparation for Roland Garros will clearly not be optimal. We'll give our best to get there in the best possible conditions to compete, but playing a grand slam without matches in Rome isn't easy.
"With the MRI we saw that something isn't 100 per cent OK. However, we have everything under control. If it doesn't get 100 per cent cured, I'll stop a little longer. Taking care of the body is more important than everything else."
