"We will not allow violent demonstrations," Inspector General of Police Japhet Koome told reporters. "The demonstrations they plan Monday are illegal and will not be allowed."
Veteran opposition leader Raila Odinga has urged people to take to the streets on Monday and Thursday for further protests against the surging cost of living in Kenya.
Last Monday's demonstrations — which were also not authorized by police — descended into violence, with riot police firing tear gas and water cannon at people hurling rocks and setting tires ablaze.
A university student was killed by police fire while 31 officers were injured in running battles in Nairobi and opposition strongholds in western Kenya.
More than 200 people were arrested, including several senior opposition politicians, while Odinga's own convoy was hit with tear gas and water cannon.
"You all saw what happened last week and we won't allow that to happen again where hooligans come to town to loot and destroy people's property and businesses," Koome said.
It was the first major political violence since President William Ruto took office six months ago after beating Odinga in an election his rival claims was "stolen."
Many Kenyans are struggling to put food on the table, battling high prices for basic goods as well as a plunging local currency and a record drought that has left millions hungry.
Ruto, who is leaving the country on Sunday for a trip to Europe, has called on the opposition leader to halt the protest action.
"I am telling Raila Odinga that if he has a problem with me, he should face me and stop terrorizing the country," he said Thursday.