Del Potro, who reached the quarter-finals at the claycourt Grand Slam event last year, flew home after losing to Frenchman Benoit Paire in the Rome Masters event last 16 last week.
"He has withdrawn," a French Federation spokesman told Reuters, confirming Argentine media reports.
"I am sad to miss such an important tournament, one that you always dream of winning," Del Potro was quoted as saying.
Del Potro is the second top-10 player to withdraw from the French Open, which starts on Sunday at Roland Garros, after Briton Andy Murray announced he would miss the tournament because of a back injury.
Former world number seven Mardy Fish, 41st in the ATP rankings, and his fellow American Brian Baker, 71st, have also pulled out.