Data protection authorities in the UK and Ireland are also conducting investigations. US-based privacy group, the Electronic Privacy Information Center, is planning to file a complaint with the Federal Trade Commission, according to the New York Times.
A spokesman for the European investigators said tags of people on pictures should happen only with prior consent. Automatic tagging will create risks and cannot be activated by default, he said.
Facebook announced earlier this week that "Tag Suggestions" was available in most countries after being phased in over several months.
The feature is active by default on existing users' accounts, but may be disabled by people who do not want their names to be automatically suggested for other people's pictures.
Facebook has defended the move by saying the feature merely assists the process of tagging photos, which is already done more than 100 million times a day.
"Tag suggestions are only made to people when they add new photos to the site, and only friends are suggested," said Facebook.
This story was first published by Computer Weekly