The message many received reads: "Your Facebook account was disabled because it did not follow our Community Standards. This decision can't be reversed."
One user told the BBC there was no warning or explanation given.
Parent firm Meta said it was investigating.
In a tweet, Meta's Andy Stone said: "We're aware that some users are experiencing issues accessing their Facebook accounts and we are working to resolve them as quickly as possible."
He did not say how many were affected, or what the issue was.
PR consultant Jen Roberts was one of those to find herself locked out of her account. She told the BBC: "I haven't posted anything or commented for quite some time, so it's extremely unlikely that I've done anything that could be construed as offensive."
But, despite not being an avid user, finding her account locked was still upsetting: "All of the images from my university years and family occasions are on Facebook.
"I will no longer have access to 15-plus years of content, which is genuinely sad.
"It is also quite stressful not knowing what the issue is, and having no recourse to resolve it. To be given no warning and then no way to access our own data is mindboggling."