The boy was showing his friend, 15, the pistol when it fired Wednesday afternoon, the Houston Chronicle reported.
The 15-year-old boy was rushed to a hospital in critical condition.
"He's lost a lot of blood. It's not a grazing wound by any means," said John Cannon, a Houston police spokesman.
Cannon said the gun was not secured and the boy found it in an unlocked cabinet.
Two other boys were inside the house at the time of the incident but did not witness the shooting, police said. The 13-year-old's mother was at work at the time.
"The family is grieving, as you would imagine. There's tragedy on both ends," Cannon said.
After an investigation by the Houston Police Department, Harris County prosecutors will determine whether to press charges against the teen in the shooting or the parents for keeping an unsecured gun in the home.