A letter from the department’s public integrity section, which investigates potential election-related law violations, went to the PAC, according to CNN.
The Justice Department and Musk’s America PAC did not immediately respond to a request for comment.
South African-born Musk, who has thrown his support behind Republican presidential candidate Donald Trump ahead of the November 5 election, announced on Saturday while speaking before a crowd in Pennsylvania that he was giving away $US1 million ($A1.5 million) each day until Election Day to someone who signs his online petition supporting the US Constitution.
He handed $1 million cheques to two separate people over the weekend – one to a man in Harrisburg on Saturday and another to a women in Pittsburg on Sunday.
Musk, ranked by Forbes as the world’s richest person, so far has supplied at least $US75 million ($A113 million) to America PAC, according to federal disclosures, making the group a crucial part of Trump’s bid to regain the White House.