The other players put on the list Tuesday were Falcons wide receiver Laquon Treadwell, and Raiders defensive end Clelin Ferrell and defensive back Lamarcus Joyner.
Treadwell is the second Atlanta player on the COVID-19 list, joining defensive end Dante Fowler Jr., who was put on it last week.
The Raiders put Ferrell and Joyner on the list Tuesday, joining linebacker Cory Littleton, who tested positive last week, and right tackle Trent Brown, who tested positive last month.
A person with direct knowledge of the situation said the player who tested positive did not travel with Washington for its game at Detroit last weekend.
The Giants and Washington were notified of their respective positive test results Monday night.