It happened around 12:15am in a fast food restaurant parking lot on Dairy Ashford near the Southwest Freeway.
Sugar Land police say the suspect and at least two other men were inside a car when they started arguing.
According to investigators, that's when the suspect pulled into the parking lot and pulled out a knife, stabbing his uncle several times and stabbing the other man in the leg.
The suspect got out of the car and tried to run, but he was found a short time later.
Police say he will likely be charged with aggravated assault.
Both victims were taken to the hospital and are expected to survive.