JAKARTA, Indonesia—A family of suicide bombers, including children, killed at least seven people and injured dozens in attacks at churches in Indonesia on Sunday, police said, the latest in a wave of Islamic State-inspired violence in the world’s largest Muslim-majority nation.

The attacks on Indonesia’s Christian minority come amid a rise in extremist violence and security lapses in a Southeast Asian nation where supporters of Islamic State have been seeking to wage large-scale attacks. It was the first time children have...