Lefeged was detained early Saturday after allegedly fleeing District of Columbia police following a traffic stop, the Indianapolis Star reported.
D.C. police spokesman Araz Alali told the newspaper the 25-year-old native of Germantown, Md., was a passenger in a white Camaro that officers had signaled to pull over for alleged erratic driving.
They said the driver of the vehicle led officers on a chase, then escaped after fleeing on foot.
Lefeged and another passenger, Timothy Wilson, 23, were arrested, and a handgun was found in the vehicle, Alali told the Star.
The pair are facing charges of carrying a firearm without license, unregistered firearm, unregistered ammunition, presence of a firearm in a motor vehicle and possession of an open container of alcohol.
They were being held in jail until a bail hearing set for Tuesday.
Lefeged, the Colts' special teams captain, has 65 total tackles and two interceptions over two years with the team.
"We are aware of the reports regarding Joe Lefeged in Washington, D.C.," the Colts said in a statement issued Saturday. "At this time, we will have no further comment on the pending matter until we gain more information."