Vincent DiBenedetto, a spokesman with the Loudoun County Sheriff's Office, said Joe Louis Joseph Jr. was booked around 3 a.m. Monday after deputies responded to a report of a single-vehicle accident shortly after midnight.
Hours earlier, Joseph and the Redskins had returned from Jacksonville following a 20-17 overtime win. Joseph played as a reserve in his first game as an active member of an NFL roster.
"We have talked with Joe and he is very remorseful for what happened and the embarrassment he caused himself, his family and the organization," the Redskins said in a statement Tuesday. "We will let the legal system run its course and withhold further comment until the matter is resolved."
Joseph, 25, joined the Redskins' practice squad Dec. 15 and was promoted to the main roster on Saturday. He spent training camp with the Tennessee Titans as an undrafted rookie from the University of Miami and was a member of the New York Giants practice squad earlier this season.
He was later released on his own recognizance. Authorities did not know if he had an attorney.
Redskins coach Mike Shanahan said he was still learning the details of the incident and would make a statement after he has spoken with Joseph.
Information from The Associated Press contributed to this report.