It happened at an apartment complex on Bennington Street near Homestead Road around 3 a.m. Thursday.
Houston police said officers were called to the apartment for a fight between a man and a woman, but when they arrived, the man had been shot in the torso and stabbed in both of his arms.
The woman was detained for questioning, HPD said.
The man was transported to the hospital and is expected to survive. The 4-year-old child was not hurt.
Investigators said the incident could have possibly been a case of self-defense. The Harris County District Attorney's Office will determine if any charges will be filed.