Fresno Police Chief Jerry Dyer said that Muhammad was in custody, and that he shouted "Allahu Akbar" ("God is great" in Arabic) when the police tackled him.
Police said they quickly arrested a suspect who they determined had previously expressed anger toward white people and the government.
"Too early to say whether or not this involves terrorism", Dyer was quoted as saying.
He says Muhammad told police he wanted to be known as someone who killed many white people and not just a security guard.
The shootings occurred within a block-and-a-half of each other, Dyer said. "These individuals that were chosen today did not do anything to deserve what they got". "These were unprovoked attacks by an individual that was intent on carrying out homicides today". The women were Latinas, he said. He said Muhammad made other statements to police but did not disclose them.
Police were alerted about the incident through the shot-spotter system.
Muhammad told officers who arrested him that he was the man they were looking for, Mr Dyer said, saying: 'I did it.
Around 10:45 a.m. local time, police officers with the Fresno Police Department responded to a scene after two gunshots were detected through ShotSpotter, a gunfire locator, according to Fresno Police Chief Jerry Dyer. A man shot and killed three people on the. He had been associated with gangs but was not a confirmed member, police say.
The man suspected of killing three people in downtown Fresno had a long record of criminal charges in Sacramento. The FBI and ATF San Francisco Field Division are assisting Fresno police with the investigation.
Muhammad used a pistol with.357 caliber rounds and used a speed loader to reload.
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Rita Katz, executive director of the SITE Intelligence Group, posted on Twitter that Muhammad's motivations may be tied to racial animus.
He surrendered to police, telling an officer: "I did it".
Dyer says he had been living on the streets and most people had "disassociated" themselves from him.
Katz also wrote that while Muhammad had posted the phrase "Allahu akbar, " his Facebook page "contains no indication of jihadi influence".
Police said the man, identified as Kori Ali Muhammad, 39, also pointed his gun at two women and a toddler in a vehicle but did not shoot. He also was wanted for a separate killing from last week, in which a motel security guard in Fresno was gunned down.
Dyer said Muhammad approached a vehicle in between shootings, but he spared the lives of two women who were in the auto with a child.
Seyed Ali Ghazvini, imam of the Islamic Cultural Center of Fresno, said Muhammad was not a member of his congregation and he did not recognize him.
In a statement, Fresno Mayor Lee Brand said: "This is a sad day for us all".
Ghazvini offered prayers to the victims and their families. They believe he went on the rampage after he saw his name released in connection to another murder he is accused of committing last Thursday. Sixteen shots rang out in less than two minutes Tuesday.
A spokesperson for the Catholic Charities told the Fresno Bee that the charity does not believe the shooter was tied to Catholic Charities.
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