The injured boy, Krissada Saeyang, who is a year and 11 months old, was admitted to Chiang Mai Hospital at 5pm.
The father, Chatchawal Saeyang, 27, and the elder son, Pichaphop Saeyang, 3, died in the alleged murder and suicide incident at their house in Ban Doi Kham village, Tambon Hang Dong, in Hod district.
The hospital said the boy was in safe condition now.
Mae Hod police chief Pol Colonel Kamkaew Suyati said Chatchawal had become depressed after his wife left him with the two sons on April 26 to get married to another man.
Preliminary investigations suggested that the father allegedly made his sons stand in a line and then fired at them with his shotgun and then turned the gun on himself.