“Honored to meet @Pontifex yesterday,” Mr Musk tweeted early on Saturday, next to a photograph of him and four of his children with the Argentinian-born pontiff.
He also tweeted a picture from Venice that appeared to be of himself with a woman, both dressed in masquerade ball costumes. Mr Musk, who has more than 100 million followers on Twitter, usually tweets prolifically and his absence from the platform had been noted.
The Vatican did not announce the audience or provide any information about what was discussed.
Mr Musk is in the process of buying Twitter for $44 billion, but since making the deal in April he has questioned the number of spam accounts on the platform, and last week said the takeover remained held up by “very significant” questions about the number of fake users on the social network.
The richest man in the world added that there were also questions about Twitter's debt and whether shareholders will vote for the deal.
The price of Tesla stock has collapsed since April, costing Mr Musk tens of billions of dollars, with investors in the electric-car company concerned that he may be distracted by his new acquisition.
Pope Francis frequently meets high-profile figures in strictly private audiences that are held in a reception room of the Vatican hotel where he lives.
A common talking point he uses when meeting with corporate chief executives is to appeal for them to use their wealth and technology to help the poorest while caring for God’s creation.
On June 21, Twitter’s board recommended that shareholders approve Mr Musk’s proposed purchase, though shares of Twitter remain far below his offer price, suggesting considerable doubt that the sale will actually happen.