A church in Mississippi popular with the African-American community was burnt and vandalised with the words "Vote Trump".
Greenville Police Chief, Delando Wilson, said someone was being interviewed in connection with the suspected arson but no charges had been laid.
Brett Carr, an FBI spokesman in Jackson, Mississippi, said the agency was reviewing whether any civil-rights crimes had been committed.
"We feel that the quote that was placed on the church was basically, it's an intimidation of someone's right to vote whatever way they choose to vote," Wilson said.
"So that would be definitely considered a hate crime." However "as far it being a racial issue," he added, "I can't say that."
Fire Chief Ruben Brown said firefighters found the Hopewell Missionary Baptist Church engulfed in flames after 9.15pm EST (1.15am GMT). The fire took about an hour to fully extinguish, The New York Times reported.
No injuries were reported and authorities are offering an $11,000 reward for information.
"Authorities are investigating and we expect a suspect will be identified and brought to justice," Mississippi Governor Phil Bryant, a Republican Trump supporter, said in a statement. "Anyone who burns a place of worship will answer to almighty God for this crime against people of faith. But they should also answer to man's law."
The Wall Street Journal reported that the incident is being investigated by the FBI, state and local law enforcement agencies, as well as the Bureau of Alcohol, Tobacco, Firearms and Explosives.
Mississippi Secretary of State Delbert Hosemann, a Republican, said that after speaking to local authorities he came to the conclusion that the acts were not committed by "somebody of a political nature."
Mississippi Democratic Party chairman Bobby Moak spoke out against the incident. "There are no coincidences in politics, and we've got a burnt-out church with political messaging on the side," he said. However he did not say if he believed a Trump supporter committed the arson. "I'm going to let local law enforcement and the local FBI office do their job."
Neither the Mississippi Republican Party nor Trump's campaign have commented.