One administrator of "secret" groups on the network raised concerns that old members would be able to access "highly sensitive" information.
Others have complained of having to leave the groups, one-by-one, again.
Facebook says the glitch would not give access to users' personal details if they were hidden via its settings.
The firm advertises the groups facility as a "private space" where updates, polls and chat messages can be shared between family, co-workers and pupils in a school class.
It adds that a group can be made "secret" to ensure that not only are messages limited to those within it, but that those outside cannot see who else is a member.
"Some users appear to have been re-added to groups that they have left in the past," the firm said in a statement.
"We are investigating the issue."
The problem comes at a time the company is involved in a separate privacy controversy.
It wants to be able to share information between its social network and its other businesses such as recently acquired photo service Instagram, and to stop its members having the right to vote on further changes to its privacy policy.
The move is opposed by campaign groups including the Electronic Privacy Information Center and the Center for Digital Democracy.
Facebook says it is investigating a fault which has seen some of its members re-registered to groups that they had quit.