After the violence, Interior Minister Kithure Kindiki issued a warning that the authorities would no longer be tolerate it.
"Lives have been lost, scores of law enforcement officers and civilians have been grievously injured and unimaginable loss to the country's economy has been occasioned," he said in a statement condemning "widespread violence, looting and destruction of private and public property".
"This culture of impunity will stop," he vowed.
Police had earlier fired tear gas on protesters in and around Nairobi, with five of the six deaths reported in the towns of Mlolongo and Kitengela on the capital's outskirts.
Tear gas was also used to disperse crowds attacking a highway connecting Nairobi to the port city of Mombasa, with one death recorded in Emali, a town located along that route.
"We have three deaths in Mlolongo, where a group of demonstrators had blocked the road to protest, and we also have two others in Kitengela and one in Emali," a police officer said.
"There was a confrontation with police officers deployed to quell the riots and some (people)... were shot in the process," he said on condition of anonymity.
A second policeman said, "I can confirm the deaths in Mlolongo, Emali and Kitengela," without elaborating further.
In Nairobi's Kangemi slum, dozens of children were hospitalised, some unconscious, after teargas was fired near their classrooms, the head of the clinic told AFP.
"We took 53 of them to the hospital and they are all now in a stable condition awaiting discharge," he said.
Opposition leader Raila Odinga, pursuing a protest campaign against the government, had urged demonstrations against a tax law that has seen fuel prices surge, adding to the difficulties faced by poor Kenyans.
But late Tuesday, police chief Japhet Koome said the authorities had not received any official notification of rallies, as required by law.
"All lawful means will be used to disperse such demonstrations," he warned.
Major roads in several western cities where Odinga commands significant support were deserted as protesters took to the streets.
'Bullets And Tear Gas'
The clashes followed rallies in several cities last week that also saw six people killed, according to the interior ministry.
Rights campaigners and opposition politicians accused police of being heavy-handed.
"We have always said that these meetings remain peaceful until police decide to break them up with bullets and tear gas," Odinga said on Wednesday.
"Police have shot, injured and killed protesters in various parts of the country including here in Nairobi."
But he said he was calling off plans to address supporters in the capital, citing fears for their safety.
The ban follows protests last Friday, when police fired tear gas in Nairobi, targeting Odinga's convoy, AFP journalists reported.
They took similar steps against demonstrations in the cities of Mombasa and Kisumu.
On Saturday campaigners said police used tear gas on civil society representatives demanding the release of dozens of people arrested during the protests.
The Kenya National Commission on Human Rights has called for an investigation into all reported incidents of police brutality, adding to condemnation from rights groups including Amnesty International over arbitrary arrests.
Odinga initiated a string of anti-government rallies this year after losing to William Ruto in presidential elections last August, a vote he claims was "stolen".
Wednesday's protest call was spurred by a new finance law aimed at generating more than $2.1 billion for the government's depleted coffers.
It provides for new taxes or increases on basic goods such as fuel and food and mobile money transfers, as well as a levy on all taxpayers to fund a housing scheme.
The high court has halted implementation of the legislation after a senator filed a case challenging its constitutional legality. The government has appealed the suspension.
Despite this, Kenya's energy regulator has already announced a hike in pump prices after the doubling of VAT to 16 percent as stipulated in the law.
Kenyans are deeply worried by the soaring cost of living, but many of those who spoke to AFP said they could not afford the disruption caused by the protests.
Shopkeeper Lameck Mwangi, 34, told AFP he had decided to close his electronics store in downtown Nairobi for the day.
"We all know where it ends when we see deserted streets like this and police patrolling town," he said.