Police say the boy, who has not been named, is co-operating with officials.
There is no indication yet on any motive nor how he obtained the weapon used, a 9mm handgun.
The shooting happened late on Monday in the town of Elkmont.
According to investigators, the boy initially called police to say he had heard gunfire coming from his family home.
He later confessed to the attack, the Limestone County Sheriff's Department said.
The victims have been named as John Sisk, 38; Mary Sisk, 36, and three siblings who were five, six, and six months old.
Mary Sisk, originally of New Orleans, was a special education teacher for the Huntsville City schools district, according to a biography of her on the Mountain Gap schools website.
School officials there say they are providing mental health counsellors to students at the school.
UPDATE: The two subjects in critical condition have died. The 14-year old caller was interviewed and confessed to shooting all five members of his family in the residence. He is currently assisting investigators in locating the weapon, a 9mm handgun that he said he tossed nearby.
Seven people were killed at the weekend in a series of random shootings in Texas, with the suspect identified as a 36-year-old man recently fired from his job.
Last month, separate attacks in El Paso and Dayton left 31 people dead
