"I'm so disappointed to have to announce my withdrawal from Roland Garros," the sixth seed said on Twitter before her match against Romania's Sorana Cirstea.
"I've had pain in my left forearm for a few weeks and last night an MRI confirmed a grade two tear which could unfortunately could get a lot worse if I play today," added the left hander.
"They said for now two to three weeks off, which means no tennis, of course, because it's my left forearm. I'm gonna do some fitness and everything what I can do and to kind of prepare my body for the tennis on the grass then.
"Of course that I'm staying positive for the grass season."
Wimbledon runs from July 1-14.
The Czech player has been replaced in the draw by lucky loser Kaja Juvan of Slovenia.
Kvitova, a semi-finalist in Paris in 2012, made a strong start to the clay court season by winning the title in Stuttgart and reaching the quarter-finals in Madrid.
A left calf injury in the third round at Rome affected her momentum heading into Roland Garros, the venue of her return to tennis in 2017 following a knife attack.
(Reporting by Simon Jennings and Shrivathsa Sridhar in Bengaluru, Julien Pretot in Paris; Editing by Peter Rutherford and Pritha Sarkar)
