The accounts will be shut down solely for being designed to promote other big social media platforms.
The company said that the move affects content from platforms.
Cross-content posting from other websites will be allowed.
It's the latest in a long line of changes since the billionaire bought the social networking site.
The Washington Post suspended reporter Taylor Lorenz for breaking the new rule before it was officially announced.
She posted a link to her account after being reinstated.
The platform many users moved to after Mr Musk's takeover had already been blocked by the social media company.
Many of our users are active on other social media platforms Free promotion of certain social media platforms will no longer be allowed.
We will remove accounts created solely for the purpose of promoting other social platforms and content that contains links or usernames for those platforms.
The details of possible violations can be found in a blog.
Attempts to circumvent the restrictions would be a violation.
If you break the rules for the first time or in an isolated incident, you could be locked out of your account.
Any subsequent offenses will result in suspension.
Advertisers will still be able to place their ads on banned sites, but users can still post content to the micro-blogging site.
Since Mr Musk bought the site, there have been a lot of changes.
Around half of its staff has been fired and he tried to roll out the paid-for verification feature in a disorganized way. Last week, the feature was re-launched.
Civil Liberties groups accuse the billionaire of taking steps that will increase hate speech and misinformation.
The EU and UN called it an attack on press freedom when he suspended a number of journalists.
The New York Times, CNN, and the Washington Post were all locked out of their accounts.