The world’s largest asset manager says companies like Facebook Inc. and Snap Inc. should put an expiration date on their founders’ supervoting powers.

BlackRock Inc. wants time or event-based sunsets at companies that use what’s known as a dual-class stock structure to keep control after going public. Such structures give ordinary investors’ shares less voting power than stock held by founders and other insiders.

“We recognize the potential benefits of dual-class shares to newly public companies as they establish themselves, however, we believe that these structures should have a specific and limited duration,” BlackRock Vice Chairman Barbara Novick said in...