Police spokesman Dustin Sternbeck said the NFL player was pulled over shortly before 3 a.m. Thursday on Interstate 66 outside of Washington and failed a sobriety test after refusing a breath test. Sternbeck says the 28-year-old was arrested and taken to a county detention center before being released later Thursday.
Meriweather signed a two-year, $6 million deal with the Redskins in March after spending 2011 with the Chicago Bears.
The 28-year-old Meriweather was a first-round draft pick by New England in 2007 and was a two-time Pro Bowl player with the Patriots before he was cut at the end of last year's training camp.
He then signed with Chicago but was a disappointment with the Bears, losing his starting job early in the season.
The Redskins need help at safety after cutting the underperforming Oshiomogho Atogwe on Monday. The team also didn't re-sign safety LaRon Landry, who is recovering from an Achilles injury and became a free agent this week.
Information from The Associated Press contributed to this report.