Vlade Divac, the Kings' vice president of basketball operations and general manager, announced the disciplinary action Thursday. The Kings said Cousins would sit out Friday's home game against the Orlando Magic.
Video from Sacramento's 120-111 home loss to the Cleveland Cavaliers on Wednesday showed Cousins sitting on the bench and in the huddle yelling and heatedly gesturing with his arm at coach George Karl, who was only a couple of feet away.
Divac was seen speaking after the game outside the locker room with Cousins, who scored a team-high 29 points and grabbed 11 rebounds in the loss. Cousins and Karl have been at odds previously.
"Obviously we try to do our best to send a message that we can't tolerate some stuff as an organization," Divac said Thursday. "He went a little far, and we have to do things to be on the same page.
"I think DeMarcus is doing very well this year. He is playing very hard. This is something where he was emotionally overwhelmed and did something that he shouldn't do."
Divac said Cousins is "a good kid, and I hate doing this."
"I don't blame him for the emotions he had, but it's the wrong thing to do," Divac said.
Divac said he didn't know details and that reporters could ask Karl about the incident Friday. Karl wasn't at Kings practice Thursday because he was undergoing a minor procedure for "a cancer" on his neck, according to the Sacramento Bee.
Karl, who has previously battled cancer, said he was treated for squamous cell carcinoma on the left side of his neck and that what was removed "was the size of a nickel. I just have to be careful for a week to 10 days."
He is expected to be back on the bench Friday, when Cousins will be serving his suspension.
The Associated Press contributed to this report.