The shooter got out of his vehicle firing an assault-style weapon, Grand Blanc Chief of Police William Renye said.
He added that hundreds of people were in the church, which was set on fire when the vehicle smashed into it.
Smoke billowed from the building as firefighters sprayed the blaze with water while fire trucks and emergency vehicles were parked nearby, footage on social media showed.
Police suspect the fire was intentionally set by the attacker.
Authorities believe they will find additional victims in the ruins, the chief said.
Police did not immediately release the name of the suspect, who died at the scene in an exchange of gunfire with two officers who rushed to the church, the chief said.
Renye described him as a 40-year-old man from Burton, Michigan.
Further details were not immediately available.
"My heart is breaking for the Grand Blanc community," Michigan Governor Gretchen Whitmer said in a statement posted to social media.
"Violence anywhere especially in a place of worship, is unacceptable," she said.
National officials, including US Attorney General Pam Bondi and US President Donald Trump, posted that they had been briefed on the shooting.
"Such violence at a place of worship is heartbreaking and chilling," Bondi posted on X.
The Church of Jesus Christ of Latter-day Saints is informally known as the Mormon church.
Grand Blanc, a town of 7700 people, is located 97km northwest of Detroit.
The shooting occurred the morning after Russell M Nelson, the oldest-ever president of The Church of Jesus Christ of Latter-day Saints, died at 101.
The next president of the Mormon church is expected to be Dallin H Oaks, per church protocol.
with AP
