Sergeant Jason Brown with the Harris County Sheriff's Office said the man asked for deputies to come to the 19500 block of Lockridge Drive because he had shot his wife.
On Sunday morning, deputies identified the man suspected in the shooting as Jeffrey Fontenot.
When deputies arrived, they found a woman dead with one or more bullet wounds, and a 10-year-old barricaded inside of a bedroom with a bullet graze wound.
The woman killed was later identified as Yashica Fontenot.
Family members said the couple had a series of on-going issues.
Jeffrey was interviewed by investigators and admitted to shooting and killing his wife after becoming angry and frustrated with her.
Sheriff Ed Gonzalez with the Harris County Sheriff's Office said Jeffrey was arrested and charged with murder and aggravated assault.
The child was released to a family member.