Police fired tear gas and arrested several senior opposition politicians in parts of Nairobi and at least one other city.
After six officers in the western town of Maseno were injured by stone-throwing demonstrators, police said security forces opened fire, killing third-year student William Mayange, who was shot in the neck and pronounced dead at the hospital.
Police officers in riot gear fired tear gas at hundreds of protesters clashed in Nairobi's vast informal settlement of Kibera, who chanted: "Ruto must go."
They also used tear gas to disperse demonstrators trying to gather in the Central Business District, from where opposition leader Raila Odinga has called for a march toward the president's State House residence, Reuters reporters said.
Police used tear gas in yet another site against protesters gathered near government offices in the heart of the capital Nairobi, where the major rally was scheduled to take place, and several other areas of the city.
"We came here peacefully but they tear gassed us," said Charles Oduor, 21, who joined the large crowds in downtown Nairobi.
"They lie to us everyday. Where is the cheap maize flour they promised? Where are the jobs for the youth they promised? All they do is hire their friends."
In the western city of Kisumu, an Odinga stronghold, police fired barrages of tear gas in the direction of protesters who had started fires in the road, footage on Citizen TV showed.
Ruto's government has vowed to take a tough stance over the protests, which opposition leader Raila Odinga insisted would go ahead despite not receiving police authorization.
Odinga called Monday for weekly protests, as clashes erupted between police and supporters demonstrating over the country's cost-of-living crisis.
"Every Monday there will be a strike, there will be a demonstration," he told crowds of chanting followers in Nairobi. "The war has begun, it will not end until Kenyans get their rights."
"I want Kenyans to come out in large numbers and show the displeasure of what is happening in our country," Odinga, who narrowly lost last year's election to Ruto, told supporters on Sunday.
Police used tear gas against protesters gathered at a site near government offices in the heart of the capital Nairobi, where the major rally was scheduled to take place, and several other areas of the city.
"We came here peacefully but they tear gassed us," said Charles Oduor, 21, who joined the large crowds in downtown Nairobi.
"They lie to us everyday. Where is the cheap maize flour they promised? Where are the jobs for the youth they promised? All they do is hire their friends."
Kenyans are suffering from surging prices for basic necessities, as well as a sharp drop in the shilling against the US dollar and a record drought that has left millions hungry.
'Life becoming more difficult'
Odinga said he had called the rallies to protest the "skyrocketing" cost of living but also the "stolen" election last August.
In Nairobi's biggest slum Kibera, a bastion of Odinga support, people also set tires ablaze while police used water cannon to disperse protesters.
Demonstrators and police also clashed in the lakeside city of Kisumu in western Kenya, another Odinga stronghold.
"Our victory was stolen and we are determined to get it back, we can't sit back and watch as life becomes more difficult by the day. We want Raila in State House," said Kevin Ojwang in Kisumu.
Nairobi police chief Adamson Bungei said on Sunday that police received requests to hold two demonstrations only late Saturday and early Sunday, when normally three days' notice is required.
"For public safety, neither has been granted," he said.
Interior Minister Kithure Kindiki warned on Sunday that anyone inciting public disorder or disturbing the peace would be prosecuted.
'Fighting for our rights'
Many businesses in Nairobi were shut ahead of the demonstrations, with some employers telling their staff to work from home.
"We are here trying to fight for our rights. Life is so hard. If you see, these young men and women, we don't have jobs, people are losing their jobs. So that's why we're talking about our rights," said shoeshiner Henry Juma, 26.
Odinga, the leader of the Azimio la Umoja party, who described Monday as a "day of destiny," continues to claim that Ruto's August election win was fraudulent and denounces his government as illegitimate.
According to official results, Odinga — who was making his fifth bid for the presidency — lost to Ruto by around 233,000 votes, one of the slenderest margins in Kenya's history.
The Supreme Court dismissed his appeals, with its judges giving a unanimous ruling in favor of Ruto, finding there was no evidence for Odinga's accusations.
Ruto has declared that he would not be intimidated by the demonstrations, saying: "You are not going to threaten us with ultimatums and chaos and impunity."
"We will not allow that," he said, calling on Odinga to act in a "legal and constitutional manner."
This report was sourced from Reuters and Agence France-Presse.