The Cowboys said Elliott suffered a hit to the head in the "minor accident" and is being evaluated. Elliott is doing conditioning work off to the side, the team said.
It's not known yet when he will be able to return to practice full time, but the team is being cautious with its star running back, who led the NFL with 1,631 yards in 2016. Elliott was a passenger in a car that was hit.
The week before the Cowboys' playoff game against the Green Bay Packers in January, Elliott was involved in a minor accident on his way to the facility.
With Elliott not practicing, Darren McFadden will take the first-team snaps.
Elliott's representatives declined comment.
The Cowboys opened up Phase 3 of the offseason program Monday and had their first 11-on-11 work Tuesday. The Cowboys hold their OTAs on Tuesday, Wednesday and Thursday for three weeks. The offseason concludes with a mandatory minicamp in June.