The vehicle caught fire after crashing into Temple Israel in West Bloomfield Township, just outside Detroit, and the man, armed with a rifle, was fatally shot by security, according to a person familiar with the matter who spoke to The Associated Press.
None of the synagogue's staff or the children at its early childhood centre were injured, Oakland County Sheriff Mike Bouchard said.
The attacker drove through a set of doors and into the hallway where something in the vehicle ignited, Bouchard said.
"He was travelling with purpose down the hall, from my look at the video," Bouchard added.
CNN, citing multiple law enforcement sources, said a large cache of explosives was found in the back of the suspect's car.
Bouchard said investigators were still searching the vehicle as well as the building for any explosives or incendiary materials.
In the minutes after the attack, smoke billowed from the synagogue.
He said one security officer was hit by the vehicle and knocked unconscious but did not suffer life-threatening injuries.
The synagogue has multiple security officers, he said, and at least one fired at the suspect, who was found dead inside his vehicle.
Allison Jacobs, whose 18-month-old daughter is enrolled in Temple Israel's day care, said she got a message from a teacher saying the children were OK even before she knew what happened.
"There are no words. I was in complete and utter shock," she told the AP. "I was hoping that it was a false report."
Temple Israel issued a statement saying all 140 students from its early childhood centre were safe.
The incident comes amid a spike in anti-Semitism in the US over the last two years.
"Anti-Semitism has no place in Michigan and cannot be tolerated," Michigan's attorney general Dana Nessel said in a statement.
"In moments like these, it's more important than ever that we come together, stand with our neighbours, confront hate whenever it appears, and build stronger communities."
"We've been talking for two weeks about the potential, sadly, of this happening. So there was no lack of preparation," Bouchard said on CNN.
"All Jewish facilities in the area are going to have a lot of extra presence around it until we figure this out."
US President Donald Trump said he had been briefed on the attack, calling it terrible.
"I want to send our love to the Michigan Jewish community and all of the people in the Detroit area following the attack on the Jewish synagogue earlier today," he said.
In a post on social media, Israel Foreign Minister Gideon Sa'ar said he was shocked by the attack.
"We are in contact with the Jewish community and local authorities. Anti-Semitism must never be allowed to rear its ugly head."
With AP
17°C