Axel Springer SE’s Stepstone employment platform asked the European Union to probe Alphabet Inc.’s Google, claiming the search-engine violates antitrust rules by downgrading results for companies that compete with its own services.

Just two weeks after Google switched on its own job search in Germany, traffic from Google dwindled, said a spokesman for Dusseldorf-based Stepstone. The company said the complaint was already filed last year once it became clear that Google would introduce its own job search in Germany.

The European Commission, the EU’s antitrust authority in Brussels, didn’t immediately reply to a request for comment. Google declined to immediately...