The world number 13, who reached the semi-finals in 2008 and quarter-finals in 2009 as well as last year, needs around three weeks to recover.
Monfils, 25, had looked likely to pull out of the second Grand Slam event of the season when he slumped to a straight sets defeat to world number 216 Brian Baker of the United States in Nice on Wednesday.
He underwent an examination in Paris on Thursday after which he decided to pull out.
Monfils will be replaced in Friday's draw by a 'lucky loser' from qualifying ahead of the start of the tournament on Sunday.
Yannick Noah was the last Frenchman to win at Roland Garros in 1983.
Injured Gael Monfils out of French Open
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