Both players can now practice without hitting, but must be been cleared by an independent neurologist before participating in any contact drills.
Tight end Brent Celek sustained a concussion in Sunday's win at Tampa Bay and won't play against Cincinnati on Thursday night.
Foles already has been named the starter for the rest of the season regardless of Vick's status. Foles led the Eagles (4-9) to their first win in more than two months in comeback fashion, 23-21, over the Buccaneers Sunday.
Brown had 347 yards rushing in his first two starts, but was held to only 6 yards on 12 carries against Tampa Bay.
Defensive tackle Mike Patterson also won't play against the Bengals because of an illness. Head athletic trainer Rick Burkholder said last week that Patterson was hospitalized with what the team believes is viral pneumonia but the condition is not related to his offseason brain surgery.
The Eagles held a walkthrough late Monday afternoon. Cornerback Nnamdi Asomugha (neck, quad), safety Kurt Coleman (chest), left guard Evan Mathis (ankle) and wide receiver Jeremy Maclin (groin) were limited.