WASHINGTON—U.S. regulators are asking Tesla Inc. whether Chief Executive Elon Musk was truthful when he tweeted that he had secured funding for what would be the largest-ever corporate buyout, people familiar with the matter said.

Officials at the Securities and Exchange Commission want to know whether Mr. Musk had a factual basis for tweeting Tuesday that the going-private transaction was all but certain, with only a shareholder vote needed to pull it off, the people said.

The...