Washington (6-7) has dropped four games in a row to lose control of first place in the NFC East and fall a half-game behind Minnesota for the sixth and final playoff spot.
Redskins head coach Jay Gruden said earlier this week that Reed may not return this season. The sixth-year tight end underwent surgery on both of his toes in the offseason.
Reed did not have a catch against New York and has a team-high 54 receptions for 558 yards and two touchdowns. Reed has dealt with a slew of injuries throughout his career and was limited to six games in 2017.
Veteran Vernon Davis is expected to draw the start in Reed's place. A former No. 6 overall pick of the San Francisco 49ers in the 2006 NFL Draft, Davis has 23 receptions and two touchdowns this year. He had four catches for 31 yards last weekend.
Washington also could be without wide receiver Josh Doctson and third-down back Chris Thompson, who are both listed as questionable for Sunday's game.
Doctson, who remains in the NFL's concussion protocol, is second to Reed on the club with 39 receptions for 469 yards and a pair of touchdowns.
Thompson, who is third on the team with 34 catches despite appearing in only seven games, is dealing with an illness.
The Redskins are down to their fourth quarterback. Josh Johnson will make his first regular-season start since 2011. Signed a week ago, he played in relief against the Giants and finished 11-of-16 for 195 yards with one touchdown and one interception.