Davis, 28, was stopped in Tysons Corner about 4 p.m. Thursday and arrested, Fairfax County Police said.
Police spokeswoman Shelley Broderick declined to discuss why Davis was stopped. A court date has not been set.
The NFL announced Wednesday that Davis was suspended indefinitely without pay. Davis, who will become a free agent next month, said in a statement Thursday that the suspension resulted from taking a supplement that contained a banned substance, not recreational drug use, which prompted his 2011 suspension.
Court records show nearly three dozen traffic-related charges against Davis in recent years.
Specifically, court records in Fairfax, Loudoun and Arlington counties and Fairfax City show 34 charges from 23 separate incidents going back to 2008, the year the Redskins drafted Davis in the second round. Twenty-one of the charges resulted in convictions, including a speeding charge for 82 mph in a 50 zone, driving on a suspended license, and numerous charges for improperly tinted windows.
The count does not include dozens of charges for failing to pay tolls, and none of the previous charges includes any allegations of drunken driving. A lawyer who has represented Davis on some of his most recent charges, Mark Dycio, was not immediately available for comment Friday morning.