Federal prosecutors indicted a high-ranking Federal Emergency Management Agency official and the former president of a Puerto Rico utility contractor, charging them with corruption in connection with repairs to the U.S. territory’s hurricane-ravaged electric grid.

The U.S. Attorney’s Office in Puerto Rico filed fraud and conspiracy charges on Tuesday surrounding a Mammoth Energy Services Inc. subsidiary that billed more than $1.4 billion turning Puerto Rico’s lights back on after its electrical system was destroyed by Hurricane...