It happened in the 3000 block of Bowser Road outside of Fulshear some time before 5:30 a.m.
The man who kicked in the door was yelling for the homeowner to shoot him, according to the Fort Bend County Sheriff's Office.
The man was shot in the leg and was believed to be intoxicated at the time of the intrusion, the sheriff's office said. It wasn't yet clear who shot him.
The home where it happened is in an unincorporated rural area of the county south of FM 1093.