A group of the extremists entered the house of the family near Ananda Bazar area and opened indiscriminate fire, killing the three on the spot, police sources said.
The assailants fled after committing the crime, they said.
The infant received bullet injuries and was admitted to hospital, the sources said.
Kokrajar had been the scene of largescale ethnic violence between Bodos and non-Bodos two years ago.