Kendrick Rayvon Fisher, 29, faces a capital murder charge.
The Houston Police Department said the stabbing happened at a west Houston apartment on Richmond Avenue on Friday shortly after 3 a.m. local time.
According to HPD, someone alerted officers that the woman and child were being held hostage inside the apartment.
Once officers arrived, they said they found Fisher asleep on a couch.
After conducting a safety sweep of the apartment, police said the 28-year-old mother and her 2-year-old were found with multiple stab wounds. They were pronounced dead at the scene.
During his arrest, HPD said Fisher was found with injuries consistent with a physical altercation, as well as blood on his clothing.
He was booked into the Harris County Jail.
The identities of the victims are pending notification to family members by the medical examiner's office, according to police.
It's unclear what Fisher's relationship was with the victims.