COLOMBO, Sri Lanka—Rampaging mobs from the majority Buddhist population attacked Muslim communities Monday night, police and witnesses said, igniting fears of a new phase of violence in Sri Lanka following deadly church bombings on Easter Sunday claimed by Islamic State.

The new attacks occurred in a cluster of towns in the country’s northwest, where the Muslim minority are often owners of shops and other businesses. In interviews, some Muslim residents said they huddled inside as the mobs approached, while others fled their...