Police said that the bodies of Nadine Carridice, 42, and her sons Jevaughn Thomas, 16, and Roshane Ellis, 11 were found with stab wounds. The throat of the mother had also been slashed.
The incident occurred in the Good Hope district, near Porus Manchester.
So far more than 200 people have been killed this year. Last year 1197 persons were murdered in Jamaica.