BAGHDAD—Six people, all from the same family, died Monday night in northwest Syria after a government plane allegedly dropped a chlorine-filled bomb on a residential neighborhood, according to residents and opposition groups.

The victims—including three young children, a mother, father and grandmother—reportedly died after being exposed to poisonous chlorine gas when a barrel bomb struck their home around 9:30 p.m. local time, according to interviews with area residents and accounts posted on social media by activists, as...