Reporters for the New York Times, CNN and the Washington Post are among those who found themselves locked out of their accounts on Thursday evening.
Meanwhile, Twitter also blocked users from sharing some links to its social media rival Mastodon – and from adding links to their Mastodon account in their bios, calling them "malware".
A Twitter spokeswoman claimed that the individual bans were due to violations of the platform’s new policy on the live sharing of location data. Mr Musk claimed that the banned reporters had tweeted his location, which he dubbed “assassination coordinates”. Most of the journalists affected had previously covered the Twitter takeover.
This comes after Mr Musk banned the @elonjet flight-tracking account set up by 20-year-old student Jack Sweeney from Florida. The account used publicly available flight data. He claimed the account put the safety of his young son at risk, and threatened legal action against Mr Sweeney while also freezing his personal account.
A spokesman for the New York Times called the suspensions "questionable and unfortunate", and said neither the paper nor reporter Ryan Mac received any explanation for the action.
“Tonight’s suspension of the Twitter accounts of a number of prominent journalists, including The New York Times’s Ryan Mac, is questionable and unfortunate,” the spokesman said. “Neither The Times nor Ryan have received any explanation about why this occurred. We hope that all of the journalists’ accounts are reinstated and that Twitter provides a satisfying explanation for this action.”
The list of banned journalists also includes Donie O’Sullivan of CNN, The Intercept's Micha Lee, Mashable's Matt Binder, and independent reporters Aaron Rupar and Tony Webster.
A CNN spokeswoman said the suspensions were “concerning but not surprising” and added: “Twitter’s increasing instability and volatility should be of incredible concern for everyone who uses [it].”
Each user’s Twitter page included a message that said it suspended accounts that “violate the Twitter rules.”
US politician Alexandria Ocasio-Cortez addressed Mr Musk directly on his own site.
She said: “You’re a public figure. An extremely controversial and powerful one. I get feeling unsafe, but descending into abuse of power + erratically banning journalists only increases the intensity around you.
“Take a beat and lay off the proto-fascism. Maybe try putting down your phone.”
Mr Musk tweeted: “Criticising me all day long is totally fine, but doxxing my real-time location and endangering my family is not.”
Doxxing is a term that refers to publishing private or identifying information about someone on the internet.
He added: “Accounts engaged in doxxing receive a temporary seven day suspension.”
One Twitter user replied, quoting a Tweet published by Mr Musk in early December, which included a photograph of his son and the words “X in beautiful San Francisco”.
He said: “Elon, I have found someone that doxxed your family and am reporting them directly to you.”
Mr Musk has previously insisted he is an advocate of free speech, tweeting “the bird is freed” on the day he took control, in reference to a loosening on regulations on the site.