Earlier in the day, a video aired on Kenyan broadcaster Citizen Television's X account showed two policemen repeatedly striking a man on the head before one of them fired at him with a long-barrelled gun as he tried to walk away.
The man fell to the ground as people in the crowd shouted: "You have killed him."
Another video aired on the Nation newspaper's website featured a witness saying the shooting victim was selling face masks and was not a protester.
Reuters could not independently verify the two videos.
A Reuters journalist saw the man on the ground with a heavily bleeding head wound, his hand clutching a packet of face masks.
It was not immediately clear if that man was the same person mentioned in the police statement.
Police Spokesperson Muchiri Nyaga said an officer who fired his anti-riot gun at a civilian had been arrested.
"Following this incident, the Inspector-General of the National Police Service ordered the immediate arrest and arraignment in court of the involved officer," Nyaga said in a statement.
Protests have erupted in Nairobi, Mombasa and several smaller towns over the death of blogger and teacher Albert Ojwang in police detention, which re-inflamed long-standing accusations of extrajudicial killings by security forces.
The state-funded Kenya National Commission on Human Rights said it had recorded 21 other injuries ranging from gunshot wounds, head cuts, whip lashes, blunt trauma and asthma attacks from inhaling teargas in Nairobi, Mombasa, Kilifi and Kwale counties.
The June 8 death of Ojwang, 31, has been a lightning rod for public discontent, a year after more than 60 people were killed during protests initially touched off by proposed tax increases.
Police first said he had committed suicide, but Kenya's Police Chief later apologised after an independent autopsy found that Ojwang's wounds pointed to assault as the cause of death.
As demonstrators took to the streets of Nairobi on Tuesday, police fired tear gas, and clashes also broke out when unidentified motorcyclists beat up protesters, dispersing them, the Reuters journalist said.
Local broadcaster NTV showed video of the bikers shouting "No protests."
Amnesty International's Kenya chapter, in a post on X, referred to the presence of dozens of motorbikes with two hooded passengers whipping protesters and members of the public.
Reuters could not immediately identify the bikers.
Nyaga referred to the group as goons. "Investigations have commenced to identify and deal with the criminals accordingly."
President William Ruto said last week that Ojwang had died "at the hands of the police", which he called "heartbreaking and unacceptable".
Ojwang was arrested as part of an investigation triggered by a formal complaint by Deputy Police Chief Eliud Lagat, according to the Independent Policing Oversight Authority watchdog.
Citizen TV said demonstrations also erupted in Mombasa, Kenya's second largest city, on Tuesday and it showed protesters shouting slogans and holding placards saying, "Stop killing us".
Last week, hundreds of people demonstrated in Nairobi over the blogger's death, with vehicles set ablaze.
Lagat said on Monday he had stepped aside temporarily, pending the completion of an inquiry into Ojwang's death.
Two senior officers and a closed-circuit TV technician, who had been called in to dismantle the CCTV at the police station where Ojwang died, have been arrested in connection with the investigation.
--Reuters--
