The Giants said Beckham underwent the surgery on Monday night.
Beckham, who was placed on injured reserve on Monday, was one of four receivers injured in Sunday's loss to the Los Angeles Chargers.
Dwayne Harris, who is also the Giants' kickoff and punt return, will undergo season-ending foot surgery. He also was placed on injured reserve on Monday.
Veteran Brandon Marshall (ankle) is also slated to undergo surgery. Marshall said on his Instagram account that his surgery will also be a season-ending procedure.
Sterling Shepard (ankle) also was hurt and is considered day-to-day.
Beckham, a three-time Pro Bowler, said on his Instagram account that he will be "back better than ever."
He was injured with about four minutes remaining when he leaped to catch a pass and the landing saw his ankle get caught beneath Chargers cornerback Casey Hayward.
Beckham had 25 receptions for 302 yards and three touchdowns this season. He is the only player in NFL history to catch at least 90 passes and accumulate at least 1,000 receiving yards in each of his first three seasons.