Fairfax County Police say 28-year-old Davis was stopped in Tysons Corner around 4 p.m. Thursday and arrested.
Police declined to discuss why Davis was stopped. A court date has not yet been set.
"I'm disappointed for Fred," Redskins general manager Bruce Allen told reporters at the NFL scouting combine. "We really can't comment on the suspension because that's a league matter with Fred. But I heard, like everyone else about what happened yesterday, and that's disappointing."
It's the second time Davis has been suspended by the NFL, and this ban could derail his career as the 28-year-old is set to become a free agent next month.
Davis claims the suspension stems from a supplement he took that contained a banned substance.
"In the past, I made the mistake of knowingly ingesting a banned substance," he said in a statement. "For over two years, I've worked very hard to eliminate marijuana from my life, and I have not had a positive test for it since 2011. Unfortunately, a couple of months ago I took a supplement that contained a banned substance. I now know that supplements are not regulated by the FDA and may contain banned substances.
"The NFL policy is strict, and not knowing that a supplement might contain a banned substance doesn't excuse a violation of the policy. I've worked closely with the NFLPA and NFL to resolve this violation, and I will be permitted to apply for reinstatement in the fall. I look forward to staying in football shape, remaining in compliance with the NFL policy and having a chance to get back on the field to contribute to a team's success next season."
Davis failed multiple drug tests in 2011 for marijuana and was suspended for four games. In May 2012, he told reporters, "You can't cry over spilled milk. The worst part of my day was losing those four games and having to sit and not help my teammates. So the worst is over, something I can learn from and something that's not going to come up again."
This is the third straight year Davis was set to enter free agency only to have a personal issue cost him. He tore his Achilles tendon during the 2012 season and re-signed with Washington on a one-year deal, rejecting a two-year contract offer from the Buffalo Bills that would have paid him about $700,000 more. Davis gambled that he would return to form and cash in this offseason.
But he caught only seven passes last season and was replaced as a starter by rookie Jordan Reed. Davis, a second-round pick in 2008, has 162 career receptions, with a career high of 59 in 2011.
Information from ESPN's John Keim and The Associated Press was used in this report.