MUNICH — Margrethe Vestager, the European Union’s antitrust chief, warned on Sunday that the collection of a vast amount of users’ data by a small number of tech companies like Google and Facebook could be in violation of the region’s tough competition rules.

Ms. Vestager’s comments are the latest in a growing chorus of European criticism about the privacy practices of American tech giants, many of which rely on crunching data based on people’s social media posts, online search queries and e-commerce purchases to fuel their digital advertising businesses.

The comments by Ms. Vestager, who, as the region’s top competition official, has sweeping powers to fine companies that are found to abuse their dominant market positions, show that European officials are stepping up their fight to strengthen data protection. In the European Union, an individual’s right to privacy is viewed on par with other fundamental rights like freedom of expression.

“If a few companies control the data you need to cut costs, then you give them the power to drive others out of the market,” Ms. Vestager said at the DLD conference, a gathering of digital executives and policy makers.