Despite Musk never being named in the tweet, he was quick to respond to Ocasio-Cortez' dig, apparently acknowledging himself as the billionaire with the "ego problem".
"Stop hitting on me, I'm really shy,' he tweeted, adding a blushing emoji.
The Tesla founder has a net worth of $US249b ($NZ385b), according to Bloomberg.
But Ocasio-Cortez said she wasn't referring to Musk. "I was talking about Zuckerberg but ok," she shot back.
Mark Zuckerberg is Facebook's founder, who has an estimated wealth of $US74b (NZ$114b), according to Bloomberg.
However, the US politician then deleted her response to Musk about a minute later.
Ocasio-Cortez later followed up on Saturday further mocking the new owner of the social media giant tweeting: "Like I said, ego problems", and posting a screen shot of her earlier tweet.
She added in another post to a user who described her response to Musk as "epic" that she deleted the tweet because "I try to avoid giving people with massive ego complexes like this the attention and QTs/replies they crave and are seeking (when I can help it)".
Many Twitter users were quick to criticise Musk after the exchange.
"This website is free, unless you're Musk, in which case it costs $44 billion and a bruised ego," one wrote.
Leaked internal communications from Twitter reveal employees at the social media platform are overtaken by despair and anger about Elon Musk's month-long effort to acquire the company.
In a statement on Tuesday, Musk said he wants "to make Twitter better than ever by enhancing the product with new features, making the algorithms open source to increase trust, defeating the spam bots, and authenticating all humans", adding that the platform has "tremendous potential".
He has also said he wants to champion freedom of speech, but critics say he has a troubled history with truth.
His employees must sign gag orders to get their jobs. He lashes out β verbally and legally β at his critics.
Media publications and even individual journalists are among his favourite targets β especially when they dare analyse his performance or behaviour.
"In reality, Twitter being owned by one person, some of whose own tweets have been false, sexist, market-moving and arguably defamatory poses a risk to the platform's future," University of Canberra social scientists John Hawkins and Michael Walsh argued.
Musk has until October to complete the Twitter takeover.
