Jacob Zachery King and Mica Marie King-Etheridge are booked into the Harris County Jail with bonds set at $50,000 each. Court records show they have no attorneys yet.
The three had been staying at a motel in the Houston suburb of Webster. Police Sgt. James Lovel says the man's sister called Webster police after she visited them and was alarmed by the boy's condition.
Police arrived, and the child was airlifted to Memorial Hermann-Texas Medical Center, where he was in critical condition Wednesday.
Lovel says Jacob King was unemployed and had come to the Houston area from Louisiana to look for work.