BRUSSELS—International Business Machines Corp. Chief Executive Ginni Rometty attacked big internet platforms for mishandling customers’ data and endorsed some European Union efforts to police the web, the latest technology chief to call out fellow companies in the debate over privacy regulation.

Ms. Rometty’s comments in the EU’s capital sought to distinguish IBM, which serves business customers, from mass-market tech companies such as Facebook Inc. and Alphabet Inc.’s Google, which have drawn attacks over data-handling from...