The violence occurred as the opposition CORD alliance resumed weekly protests aimed at seeking a shake-up of the country's electoral commission, which they accuse of bias.
A bullet wound was visible on the corpse, which was laid outside a hospital morgue by protesters, who said he was hit when police opened fire.
There was no immediate response from police.
The Red Cross said six protesters had been taken to hospital suffering from gunshot wounds.
"This is not fair. We cannot have police shooting people every other time they are exercising their rights, this man has been shot dead while protesting," said protester Michael Omondi.
Protests organised by the CORD grouping began in April to force a change of leadership at the country's Independent Electoral and Boundaries Commission (IEBC) ahead of presidential polls due next year.
The protests were briefly suspended late last month to allow for talks with the government but resumed today.
Nairobi's police chief Japheth Koome warned over the weekend that police were prepared to use lethal force if necessary.
"That's why I'm questioning those who have intentions of demonstrating... Don't come, then you start talking about police brutality. Life is dear! Please, if you value your life, don't attempt it that way. You will be dealt with firmly."
However, the High Court said early today that the protest was deemed legal.
CORD leader Raila Odinga has blamed the commission for his defeat in 2013 by President Uhuru Kenyatta.
Next year's August election is shaping up as a replay of 2013, with 71-year-old Odinga again aiming to unseat Kenyatta, 54.