Open the Messenger app
Tap your profile picture
Tap Account settings or Meta Accounts Center
Go to Personal details
Tap Account ownership and control
Tap Deactivation or deletion
Select the Facebook account linked to Messenger
Choose Delete account
Follow the on-screen prompts to confirm
If you only want to remove the app, uninstall Messenger from your device
On iPhone, press and hold the Messenger app, then tap Remove App
On Android, press and hold the Messenger app, then tap Uninstall