When asked on Twitter whether he was serious, Musk replied: "Yes".
Tesla did not immediately respond to a request for comment.
$420 per share would be a significant premium on where Tesla is now trading, and also its performance over the first half of the year.
The BBC has been unable to verify the post was written by Mr Musk himself, but it has pushed the shares 6% higher. "Funding secured", Musk tweeted shortly before 1 p.m. on Tuesday. The company had a market value of $58bn as of Monday's close.More news: Derek McInnes: 'Rangers striker Alfredo Morelos deserved red card'
More news: Johnny Depp's Biggie Smalls biopic gets shelved
More news: Note 9 leak may have just unveiled the whole package
Musk's surprise announcement comes as the Financial Times revealed that a fund controlled by the Saudi Arabian government holds a stake of between three and five percent in the company.
"I believe Tesla considers Tweets as public disclosure". According to the Times, the Saudis recently approached Musk and offered to buy even more Tesla shares, an offer that Musk refused.
"I can't believe this is something to bluff or make fun of". He said is considering taking the company private at $420 a share and already has secured funding.
"Details, structure, participants and how the valuation has been determined remain to be seen".