"No structural damage besides the meniscus tear, so the return should be quick," Rapoport added.
Gallup was off to a strong start to the 2019 season with 13 catches for 226 yards through two games. He currently ranks fourth in the NFL in receiving yards.
The 2018 third-round pick showed plenty of promise as a rookie last season, finishing with 33 catches for 507 yards and two touchdowns, ranking second on the team with 15.4 yards per reception.
Gallup also came up big in the playoffs, with 119 receiving yards in a second-round loss to the Los Angeles Rams.
The latest injury is a setback after the 23-year-old's hot start, but it's clear he can remain an important part of the Cowboys offense when he returns.
Dallas still has two established receivers on the roster in Amari Cooper and Randall Cobb, although depth is now a significant problem with Dak Prescott only completing four other passes to receivers so far this season. Three of those went to Devin Smith, who scored his first touchdown since 2015 in Sunday's game against the Washington Redskins.
Smith and Tavon Austin will likely see more playing time while Gallup is out, although the tight ends and running backs will also feature prominently in the passing attack.