Facebook Inc. said Wednesday it will start removing misinformation that could spark violence, a response to mounting criticism that the flow of rumors on its platform has led to physical harm to people in countries around the world.

The new policy is a shift in Facebook’s broader approach to misinformation, which until now has been focused on suppressing its popularity on the platform without scrubbing the problematic content entirely. But the company has also faced more questions about the platform’s role as a vector for...