The case related to Facebook's 2020 acquisition of Gif-sharing service Giphy, which is under investigation.
The CMA said Facebook had not provided information, ignored many warnings, and committed a "major breach". The firm denies deliberately breaking rules.
There are also reports that its parent company might change its name.
Tech news site The Verge revealed the news about the firm - which owns the Facebook service itself, as well as WhatsApp, Instagram, Oculus VR, and other brands.