NFL Network's Kimberly Jones first reported the news.
Beckham was one of four Giants wideouts to exit Sunday's game due to injury along with Marshall, Harris and Sterling Shepard. Both Marshall and Harris will miss the rest of the season, and New York also confirmed they underwent surgery Tuesday.
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The 24-year-old Beckham has been among the most dynamic receivers in the NFL since he entered the league in 2014 as the No. 12 overall pick.
In each of his first three seasons, Beckham was named to the Pro Bowl and finished with at least 90 receptions, 1,300 yards and 10 touchdowns.
Beckham appeared in four games in 2017 after missing New York's opener due to injury. He registered 25 catches for 302 yards and three scores.
OBJ will play under the fifth-year option on his rookie contract next season before reaching free agency in 2019.
The Giants fell to 0-5 after Sunday's loss, and the offense could be in for an even greater struggle moving forward with Beckham, Marshall and Harris on the shelf.
Shepard figures to be the No. 1 target for quarterback Eli Manning, while unproven receivers Roger Lewis and Tavarres King will get increased opportunities, as will rookie tight end Evan Engram.