Opposition supporters boycotted the election and clashed with police, forcing authorities to postpone voting in some areas.
Henry Makiwa, from the Christian charity World Vision UK told Premier that staff were in touch with a representative in the East African country and he asked that people pray for the nation.
He said: "This political process and the reports we are getting on violence is not so good and doesn't bode well for the future, safety and protection of the children of Kenya."
A source said one person was killed in the opposition stronghold of Kisumu County, another in Homa Bay in the west, and the third in Athi River town outside the capital, Nairobi.
Authorities have postponed voting in several counties until Saturday because tear gas, burning barricades and gangs of young people preventing voting in some towns.
However, Mr Makiwa told Premier young people shouldn't be held responsible for violence in the country.
He explained: "At the core of our work is the children themselves who are very often, never the cause of violence - especially of a political nature but always the victims."
While most of Kenya was peaceful, voter turnout was relatively low even in some regions considered to be strongholds for President Uhuru Kenyatta, who was declared the winner of an 8th August election that later was nullified by the Supreme Court.
Opposition leader Mr Raila Odinga, whose legal challenge to the election results led to the vote being nullified, withdrew from the new election, saying the process was not credible because of the lack of electoral reforms.
Mr Makiwa said the country has already "been facing a much bigger crisis" that could get worse if peace isn't restored.
Speaking about the country's problems, he added: "They've had a drought; they've had some food shortages. Right now at the moment there are 3.5 million people who are next to starving.
"If things don't go so well - if we do not see peace - this situation is likely going to be exacerbated."
Many observers say Kenya's ethnic-based politics undermine its democracy.
Mr Kenyatta, who got 54 per cent of the vote in August, is from the Kikuyu group; Mr Odinga, who got nearly 45 per cent in the earlier election, is a Luo.
Makiwa said World Vision and other NGOs were praying for children in Kenya.
Speaking about his specific prayer points, he told Premier his hopes: "All the actors involved, including the non-state actors as well - put the children's safety and protection at the core of proceedings from today and into the future.
"But we also have to remember that beyond the political process, Kenya has also been facing a much bigger crisis.
"We had set out way back in...2015 that our strategic goal would be putting those children at the core of our work, increasing protection [and] their participation in building the nation of Kenya and ensuring that the wellbeing of 2.6 million vulnerable children is taken into consideration."
Listen to Henry Makiwa speaking with Premier's Tola Mbakwe:
