Monfils, who was due to face Rune in Thursday's night session on Philippe Chatrier court, said he had received medical advice not to play any more at the French Open.
"Physically I woke up quite good today," said Monfils, who had spent almost four hours on centre court on Tuesday evening. "But I had a problem with my wrist that I cannot solve. I felt it during the match yesterday," he told reporters.
"I came back from my an examination and the doctor said it was not good to play with this type of injury. Yesterday it was risky. Today he said I should stop."
Monfils, a former semi-finalist and three-time quarter-finalist at Roland Garros, missed much of last season due to heel surgery.