The company said on its website that it would “remove any free promotion of prohibited third-party social media platforms, such as linking out [using URLs]” .
The list of rivals mentioned by Twitter include Facebook, Instagram, Mastodon, Truth Social, Tribel, Post and Nostr.
TikTok was not included.
“Specifically, we will remove accounts created solely for the purpose of promoting other social platforms and content that contains links or usernames” to the listed platforms, Twitter said.
Twitter listed examples such as “follow me @username on Instagram”, “email@example.com” as ones that would result in removal.
Mr Musk, who has sought to portray himself as a free-speech absolutist, recently disbanded Twitter's Trust and Safety Council and banned several accounts of users who were critical of him.
The move drew condemnation from journalists and world leaders.
He later reversed the bans. Mr Musk said the accounts were removed for sharing his real-time location.