The story was first reported by The Washington Post.
Police stopped Blanche's car on Interstate 85 in southern Virginia. He was driving 86 mph in a 70-mph zone, police said.
Brunswick County 1st Sgt. Dwyane Jones told The Post that that anyone caught driving more than 80 mph in Virginia can be charged with reckless driving.
Blatche, who was released on $2,500 bond, was "very cooperative," Jones told The Post.
"We are obviously disappointed in Andray's actions and expect him to use better judgment, especially in light of his past incidents," Wizards president Ernie Grunfeld said. "However, we will handle this matter internally and will have no further comment."
Blatche, who signed a five-year contract worth approximately $15 million last year, has been in trouble with the law before.
Last summer, Blatche and another man were accused of trying to solicit sex
from an undercover police officer, and Blatche was also wanted for
failure to appear on a charge of driving without a license.
The solicitation charge was dropped after Blatche followed orders from the court and completed a program to educate men who solicit prostitutes.
Blatche was a second-round draft pick out of high school in
2005, but he missed training camp after he was shot in a carjacking
attempt in the Washington suburbs. He split time during the 2005-06
season between the Wizards and Roanoke of the D-League.
Blatche enjoyed his best season in the NBA in 2007-'08, playing in all 82 of the Wizards' games and averaging 7.5 points and 5.2 rebounds.
Information from The Associated Press was used in this report.