The attacks came hours after police raided two mosques they accuse of having links with militant Islamists in neighbouring Somalia.
One person was killed in the police raids and more than 200 were arrested.
Witnesses said masked youths armed with machetes then went on the rampage in the Kisauni area of the city, attacking people waiting at bus stops.
Several others were injured in the attacks, which were carried out in apparent revenge for the police action.
"We are investigating the incident and have arrested some of the suspects," local police chief Richard Ngatia said.
Some of the youths were reported to be carrying black flags similar to one recovered in the raids on the Musa and Sakinah mosques.
Police said they had also seized a pistol and a cache of ammunition, including grenades, in the raids.
They say the mosques have links with the Somali militant Islamist group, al-Shabab, and have been used to recruit and train militants and store weapons.
Muslim clerics and human rights groups have condemned the raids, which they say will only reinforce feelings that police are targeting the entire Muslim community in Mombasa.
In February, a similar raid at the Musa mosque led to violent protests. The mosque was once controlled by the radical cleric Sheikh Abud Rogo, who was killed in 2012.
There have been a number of bombings and shootings in Mombasa since 2011 when Kenyan troops entered Somalia to attack al-Shabab.