The reveal came in response to a tweet claiming Musk's private jet had arrived in Hawaii on Sunday amid the final week of Tesla's fiscal fourth quarter. Ellison relocated to the Hawaiian island of Lanai earlier this month, where the billionaire owns roughly 98% of the land.
Musk added that he would be "back working on Tesla end of quarter" on Tuesday.
Representatives for both Musk and Ellison did not immediately return FOX Business' request for comment on the meeting.
Musk recently disclosed he has personally relocated to Texas after he chose Austin to build a Tesla factory. The electric vehicle maker still maintains a factory in California, however, Musk has expressed his displeasure with the state.
Earlier this month, Musk compared California to a successful sports franchise that has become too used to winning.
"If a team has been winning for too long, they do tend to get a little complacent, a little entitled, and then they don't win the championship anymore," he said. "So California has been winning for a long time, and I think they are taking it for granted a little bit" he said during an interview Wall Street Journal editor-in-chief Matt Murray at a CEO Council Summit.
Ellison, who joined Tesla's board in 2018, is the second-largest individual shareholder in the company behind Musk himself.