The shooting took place inside the apartment at 10700 Fuqua in southeast Houston around 12:45 p.m. Monday, according to police.
Police tell ABC13 paramedics took the boy to Texas Children's Hospital for treatment.
The boy was alive when he was transported, according to police.
"We're investigating the scene. We have the Houston Forensic Center out here taking evidence to make sure we're as thorough as we can be," Houston Police Captain Derrick Small said.
The boy's parents and an infant were also inside the home at the time of the shooting, HPD said.
Houston police say detectives are questioning the boy's parents about the circumstances that led to the shooting.
The infant is fine and is currently with another family member.
"It's a time to remind the public to make sure we secure and store our firearms in a way to keep our children safe," Captain Small said.