Police were called out just after 5:30 pm Saturday to the Target on Henderson Avenue and Prospect Street.
Investigators say the two teens were involved in a fight when the 15-year-old pulled out a knife and stabbed the victim twice before fleeing the scene.
The victim identified the suspect, and detectives later obtained a search warrant for the suspect's home.
Officers located the knife used in the stabbing inside the 15-year-old's bedroom.
The teen was later arrested and booked into the Tulare County Juvenile Detention Facility.