Stanton suffered a knee injury this past week during practice.
Running back Dontrell Hilliard, who suffered a concussion in last week’s 43-13 loss to the Tennessee Titans was ruled out for the game Saturday.
D’Ernest Johnson is expected to replace Hilliard in the backfield and in the return game.
Moving Stanton to injured reserve elevates Garrett Gilbert to the backup quarterback role.
Gilbert and Johnson both came to the Browns from the now defunct Alliance of American Football where they played for the Orlando Apollos.
McGuire, in his third NFL season, was a sixth-round pick in the 2017 NFL Draft by the Jets. He has appeared in 24 games, five starts, and carried 180 times for 591 yards and four touchdowns to go with 36 catches, 370 yards and two TDs receiving.