He will not be suspended.
Cousins apologized in a statement released through the Kings.
"There is a time, place and manner to say everything, and I chose the wrong ones," he said in the statement. "Like most people, I am fiercely protective of my friends and family, and I let my emotions get the best of me in this situation. I understand my actions were inexcusable and I commit to upholding the professional standards of the Kings and the NBA.
"I apologize to my teammates, fans and the Kings organization for my behavior and the ensuing distraction and look forward to moving on and focusing on basketball."
The team reviewed an incident in which Cousins confronted and shouted obscenities at the Bee's Andy Furillo over a column that referenced the arrest of Cousins' brother.
"The Kings have a clear set of standards of conduct expected of our entire organization," the team said in the statement. "As a result of negative interactions with certain members of the media that were not corrected after verbal warnings, we have decided to impose a substantial fine. If this behavior is repeated again we will be forced to consider further discipline."
The column, published over the weekend, addressed an incident at a New York nightclub earlier this month that resulted in Cousins and teammate Matt Barnes being sued over an alleged assault. It also referenced an incident at a bar in May involving Cousins and his younger brother, Jaleel, that led to Jaleel's arrest.
Kings coach Dave Joerger said he is "not going to spend another thought" on the issue. On Monday, Joerger called Cousins' actions "excessive" but also said he did not think the Bee was practicing fair reporting in regard to Cousins.
"I think we dealt with it and the more you talk about it, the bigger it exasperates itself," Joerger said before the Kings played Portland on Tuesday night. "I said what I had to say on it, moved on. DeMarcus had to say what he had to say on it and we roll on."
Cousins had 55 points and 13 rebounds in a 126-121 win over the Blazers on Tuesday night. He was ejected for apparently spitting out his mouthpiece after being fouled with 35 seconds left in the game.
After Cousins went to the locker room, officials huddled and decided to rescind the ejection. Cousins returned to complete a three-point play and put the Kings up 122-119.
Cousins refused to address the fine after Tuesday night's win, simply smiling and giving a thumbs-up when questioned about it.
Information from The Associated Press was used in this report.