This comes just one day after Davis was suspended indefinitely for violating the NFL's substance abuse policy.
According to the Fairfax County Police Department, Davis was stopped around 3:45 p.m. near Gallows Road and Leesburg Pike, located in Tysons Corner. The police would not go into further detail.
"I'm disappointed for Fred," general manager Bruce Allen told reporters at the NFL Scouting Combine.
Allen did however have something positive to say about Davis. "He had to overcome a hurdle a few years ago, and he did it. He got injured and he worked hard to come back, and so it's up to Fred what his future holds."
Davis has managed to assemble quite the track record for himself. In 2011, the league suspended him for the remaining four games of the season after failing multiple tests for marijuana use.
The 28-year-old was set to become a free agent in March after signing a one-year contract with the Redskins last season.
Davis, a once promising tight end, now with six seasons under his belt, has totaled 162 receptions for 2,043 yards and 13 touchdowns. To put these numbers into perspective, New Orleans Saints tight end Jimmy Graham managed 171 receptions for 2,197 yards and 25 touchdowns in the last two seasons.
Washington attempted to trade Davis before the deadline, but no team had much interest. At this point, he may want to start filling out applications for a summer job before the high school students do.