Those companies and others have European head offices in Dublin, and the UK's exit from the EU will change its legal relationship with Ireland, which remains in the Union.
Outage tracking website Downdetector.com showed earlier in the day that there were more than 4,600 incidents of people reporting issues with Messenger and over 900 reports on Instagram.
Facebook also bought Giphy, a popular website for making and sharing animated images, or GIFs, in May. That acquisition has already drawn scrutiny from the United Kingdom's competition watchdog.
With the filing of the twin lawsuits, Facebook becomes the second big tech company to face a major legal challenge this fall.
The FTC said in a statement that it would seek an injunction that "could, among other things: require divestitures of assets, including Instagram and WhatsApp."
Snapchat launches a new section of its app called the Spotlight, which will showcase user-created video, and offer serious competition to Instagram Reels and TikTok.