All the shootings were random, unprovoked attacks and while the victims have not been identified, Dyer said they were all white males.
Muhammad is believed to have carried out a fatal shooting last week at a Fresno Motel 6, as it was caught by surveillance video.
Muhammad's alleged shooting spree began around 10:45 a.m. when police say he shot a man in a utility truck.
The second shooting was shortly after, during which the gunman fired a number of rounds at a man, killing him. All three victims in Tuesday's killings were white men, and Muhammad is black.
"Immediately upon the individual seeing the officer he literally dove onto the ground and was taken into custody.as he yelled out 'Allahu Akhbar, '" police chief Jerry Dyer said at a press conference held on the same day, according to local news outlet ABC30.
A man shot and killed three people on the streets of downtown Fresno on Tuesday, shouting "God is great" in Arabic during at least one of the slayings and later telling police that he hates white people, authorities said. The imam said he is consulting with other faith leaders. He said that members are shocked. All three of his victims in Tuesday's killings were white, Dyer said, noting that two of the victims shot outside the Catholic Charities are believed to have been clients of the social service agency, not employees.
The Fresno Bee newspaper reported that the gunman opened fire with a handgun while cursing shortly before 11am (1am Wednesday, Thailand time) near a Catholic Charities building. "We offer condolences for the victims, we pray for the victims and their families".
County government buildings were placed on lockdown and residents were urged to shelter in place, according to the newspaper.
The suspect, who was armed with a revolver, then dropped shell casings and reloaded his gun before he set off to Catholic Charities on North Fulton Street in Fresno, Dyer said.