Two Canadian brothers and their money-service business allegedly processed $250 million in transactions without a license on behalf of customers, including Ponzi schemers and a child pornography website, according to U.S. prosecutors.

Firoz and Fehran Patel, who live in the Montreal area, were charged in Washington, D.C., federal court with operating an unlicensed money-service business, money-laundering conspiracy and violating compliance requirements. Their company, MH Pillars Ltd., which did business as Payza, also was...