McCoy started two weeks ago against the Seattle Seahawks when Jones was unable to play due to a hamstring injury suffered against the Cincinnati Bengals. McCoy completed 13 of 22 passes for 105 yards as the Giants upset Seattle, 17-12.
Jones played last Sunday against the Arizona Cardinals, but suffered an ankle sprain in addition to his hamstring injury.
The Giants (5-8) are in the midst of a fight for the NFC East title. The Washington Football Team (6-7) is in first place.
Oddly, none of the teams in the division will play Sunday with their starting quarterbacks. Dwayne Haskins will replace the injured Alex Smith for Washington, Jalen Hurts has replaced Carson Wentz in Philadelphia and Andy Dalton is playing in place of Dake Prescott for Dallas.