Both players are vaccinated, so their status for Sunday's game against the New England Patriots remains in question. Each player would need two negative tests 24 hours apart to play.
The Browns announced Tuesday afternoon that they had placed both Chubb and Felton on the reserve/COVID-19 list.
The Browns had another running back, John Kelly, go on the reserve/COVID-19 list Monday.
Chubb, a two-time Pro Bowl selection, rushed for 137 yards and two touchdowns in the Browns' 41-16 victory over the Cincinnati Bengals on Sunday and leads the team with 721 rushing yards and six rushing touchdowns this season.