Sweeney was driving his 2004 BMW sedan when officers noticed him abruptly swerving out of the lane, the Albany Times-Union reported Monday.
Lt. Scott Coburn said officers smelled alcohol on Sweeney's breath and gave him a field sobriety test, which he allegedly failed.
A test of his blood-alcohol content showed 0.18 percent, more than twice New York's legal limit of 0.08 percent, police said.
Now, the 52-year-old Republican faces misdemeanor charges of driving while intoxicated and aggravated DWI. The second charge carries a maximum penalty of a year in jail.
"I regret the occurrence," Sweeney said in a statement given to the New York Daily News. "I deeply apologize to my family and friends. I take full responsibility and I am hoping to work for a fair resolution."
Sweeney failed to be re-elected in 2006.
Police: Sword-wielding man demanded free tacos
Campus cop fatally shoots Texas student during traffic stop