"The doctors say if I play tomorrow maybe it can be dangerous," the Italian said, calling his decision "difficult" and adding he had his leg checked by a doctor only 20 minutes earlier.
Fognini beat Albert Montanes of Spain 4-6, 6-4, 3-6, 6-3, 11-9 Sunday to reach his first Grand Slam quarterfinal.
While trailing late Sunday, Fognini winced in pain at the baseline after hitting a serve and clutched at his left leg. He had his leg massaged and resumed, but eventually had his troublesome thigh wrapped in a bandage.
"(The match) was really incredible, it was really long. At the end I was not really good," Fognini said. "But I did some examinations after the match. I was crying after the match, also for the pain, but I think that's normal."
While trailing 7-6 and serving at 15-30 — meaning Montanes was two points from victory — Fognini hurt his leg. He called for the trainer and sat down in his changeover chair for a massage while play was halted. When action resumed, Fognini won three points in a row to hold serve for 7-all.
The match lasted 4 hours, 22 minutes.
"I never think to retire," Fognini said.
The 24-year-old Fognini is Italy's first man to reach the French Open quarterfinals since 1995, and first to make it this far at any major tournament since 1998.
"I'm not really happy right now," Fognini said. "It's the best tournament of my career."
Djokovic is 41-0 in 2011 and has won 43 straight matches, but he will not be credited with a victory over Fognini because the Italian withdrew. That means he would have to wait until after the French Open — assuming he won it — before getting the chance to equal Guillermo Vilas' overall Open era record of 46 straight victories.