Massachusetts election officials described the incident as a "deliberate attack."
Boston Police said on Monday they had arrested a 39-year-old Boston man in connection with the burning of a ballot box early on Sunday.
Police charged Worldy Armand late on Sunday on an outstanding warrant for receiving stolen property, Boston Police Department said in a statement.
Armand was charged early Monday with willful and malicious burning, and was scheduled to be arraigned in Boston Municipal Court, police said. No bond was set.
The FBI is also investigating the fire set on Sunday and said the ballot drop box was in front of the Boston Public Library.
Massachusetts election officials described the incident as a "deliberate attack."
There were 122 ballots inside the box when it was emptied Sunday morning, and 35 were damaged, officials said.
Boston Mayor Marty Walsh called the incident a "disgrace to democracy, a disrespect to the voters fulfilling their civic duty, and a crime."
Crews put out the fire by filling the ballot box with water, the Boston Police Department said in a statement.
"It is a top priority of our offices to help maintain the integrity of the election process in Massachusetts by aggressively enforcing federal election laws", the FBI said in an announcement of the investigation.
Voters whose ballots were affected can vote in person or via a replacement ballot that will be mailed to them, officials said.
Early voting began last Saturday in Massachusetts, and more than two million residents have already cast their ballots in person or by mail.
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