A state trooper gave Katz a summons after a traffic stop Thursday morning, the Albany Times-Union reported.
State Police said Katz was pulled over after the trooper observed him driving 80 mph near Coeymans, a town in the Albany area.
"After noting the odor of marijuana, a New York State Trooper found Katz in possession of a small bag of marijuana," a State Police's press release states.
Katz, who represents the Lower Hudson Valley, sits on the Assembly Alcoholism and Drug Abuse Committee. He voted in January against legalizing medical marijuana in New York.
Katz is scheduled to appear in municipal court in Coeymans March 28.
His office released a statement Friday calling the traffic stop and ticket an "unfortunate incident," The New York Times reported.
"This should not overshadow the work I have done over the years for the public and my constituency," Katz said. "I am confident that once the facts are presented that this will quickly be put to rest."