Two victims died from gunshot wounds, Grand Blanc Township Police Chief William Renye told a news conference on Sunday.
The fire caused extensive damage to the building and some people remained unaccounted for, Chief Renye said.
Earlier, he said "hundreds" of people were attending services at about 10:25 local time (15:25 GMT) when a gunman drove a vehicle into the building.
The attacker then opened fire with an assault-style rifle, "firing several rounds at individuals within the church," he said.
The police responded immediately to the scene, he said, adding officers "engaged in gunfire with that particular individual, neutralising that suspect". He was killed at 10:33 local time, eight minutes after the shooting.
"We are still trying to determine exactly when and where the fire ended up coming from and how it got started," the police chief said. "We believe it was deliberately set, though, by the suspect."
Chief Renye also praised the "heroism" of churchgoers who he said had sheltered children in the church during the incident.
Investigators are conducting a search of the suspect's property and examining his cell-phone records as they work to establish a motive.
The FBI is leading the investigation and has deployed crisis response teams, bomb technicians and others to the scene, according to Reuben Coleman, the acting special agent in charge of the FBI's Detroit field office.
Michigan State Police spokeswoman Kim Vetter told reporters that officers have been responding to additional bomb threats at multiple other locations.
"We've responded and cleared those locations," she said.
In a statement, the Church of Jesus Christ of Latter-day Saints confirmed a gunman opened fire during worship services, and "multiple individuals were injured".
"We pray for peace and healing for all involved," it said.
Grand Blanc police said that 100 FBI agents have been deployed to assist with the investigation.
President Donald Trump said he had been briefed on the shooting, and confirmed the FBI will be leading the federal investigation.
Writing on Truth Social, he described it as "yet another targeted attack on Christians in the United States of America".
US Attorney General Pam Bondi said in a post on X that she had received briefings on "what appears to be a horrific shooting and fire" at the church.
"Such violence at a place of worship is heartbreaking and chilling," Bondi said. "Please join me in praying for the victims of this terrible tragedy."
Michigan Governor Gretchen Whitmer condemned the incident, saying: "Violence anywhere, especially in a place of worship, is unacceptable," adding that she was monitoring the situation.
Mitt Romney, former US senator for Utah and one of the most prominent Mormon politicians, called the shooting a "tragedy", adding: "My brothers and sisters and their church are targets of violence. Praying for healing and comforting."