The boy was rushed to hospital but died. His victim, who was not known to him, is said to be in a serious but stable condition.
"At this stage, it appears that he acted solely and alone," Western Australia Premier Roger Cook said, BBC reported.
Police in Western Australia said they received a call late on Saturday from the teenager who had warned them he intended to commit "acts of violence".
Police commissioner Col Branch told a press conference that within minutes another emergency call was received alerting officers that a "male with a knife was running around the car park" in Willetton, a southern suburb of Perth.
Three officers arrived and found a 16-year-old armed with a long kitchen knife.
The first two officers fired their Tasers but when the teenager continued to approach, the third officer fired a single shot which killed the 16-year-old, the commissioner said.
SD/PR