Thompson was suspended for Washington State's regular-season finale Saturday against UCLA.
"We are aware of the situation involving Klay and will continue to gather information," Washington State coach Ken Bone said in a statement released Friday. "Klay will be suspended for Saturday's game against UCLA and the situation will continue to be evaluated throughout the weekend. Until that time neither myself nor the team will have further comment."
Thompson was cited with the misdemeanor charge of marijuana possession after police pulled over his GMC Envoy at 11 p.m. PT near campus for a headlight that wasn't functional, commander Chris Tennant of the Pullman Police Department told ESPN.com Friday.
Washington State beat USC 85-77 earlier in the night.
Tennant said Thompson was alone in the vehicle and the police officer smelled the odor of marijuana. He said Thompson denied that there was marijuana. But Tennant said 1.95 grams of marijuana were found in the vehicle, which was impounded but returned to him early Friday.
Tennant said Thompson, who was released at the scene, would receive a date to appear in Whitman County District Court within two weeks. Tennant said Thompson's court date likely would be within a month.
Thompson averages a team-high 21.4 points and is a contender for first-team all-Pac-10 honors. The 6-foot-6 junior wing is the son of former NBA forward Mychal Thompson, who is a contributor and color commentator on Lakers' radio broadcasts on 710ESPN in Los Angeles.
"I can't put into words how disappointed I am in my son," Mychal Thompson said in an interview on the Max & Marcellus Show on 710ESPN.
"He said, 'It ain't mine,'" Mychal Thompson said. "... Doesn't matter. It's in his car. Marijuana is in the car, it's his car, the marijuana is his as far as I'm concerned. Plain and simple. That's the way the law looks at it."
Washington State is considered a possible bubble team for the NCAA tournament after winning at Washington Sunday. Thompson scored 26 points in that win. The Cougars (19-10, 9-8) are considered a possible Pac-10 tournament sleeper to win the title and earn the automatic berth.
"He has embarrassed himself, let down his teammates and his school," Mychal Thompson said in the radio interview.
Earlier this season, Washington State guard Reggie Moore was suspended for one game for a similar marijuana possession arrest in early January.
Senior writer Andy Katz covers men's college basketball for ESPN.com.