"He was brought here with a gunshot wound to the upper thigh. He died in the hospital," a source at Jaramogi hospital told AFP, identifying him as 19-year-old George Odhiambo and saying he had died of massive blood loss.
An AFP correspondent at the hospital also saw his body.
A senior police source confirmed the information and said a second protester had been killed, but AFP was unable to immediately confirm the report.
The hospital source said at least four people with bullet wounds had been admitted for treatment as well as another two with minor injuries who had been beaten by police.
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Meanwhile, a man was stabbed and seriously wounded while on his way to vote in the coastal city of Mombasa, police chief Benjamin Rotich said.
"We are investigating the matter, but no suspect has been arrested so far," he said, indicating the attack happened in the southern area of Likoni.