The boy was found critically injured outside Craigieburn Community Hospital in Melbourne's north, about 7.50pm on Wednesday.
A staff member from the clinic rushed to his aid and delivered CPR, but he died at the scene.
In a statement released on Wednesday night, police said a crime scene had been established and the boy, from Mickleham, had yet to be formally identified.
About 5.30am on Thursday, a 16-year-old boy and a 20-year-old man were arrested in the nearby suburb of Pascoe Vale.
They will be interviewed by homicide squad detectives.
Investigators were on Thursday afternoon continuing to gather evidence and were seen door-knocking nearby homes.
A young man was seen arriving outside the clinic to place a framed picture of the dead boy and a bunch of white flowers.
A bouquet of yellow flowers was also left on a nearby bench, with a note asking "when will these postcode wars end?"
"Another senseless, tragic life taken far too soon. RIP dude," the note read.
"Love + thoughts are with your family + friends."
Northern Health, which operates the medical centre, said it had no knowledge of the circumstances leading up to the young man being found.
"A staff member discovered a young man in the hospital car park with serious injuries," an organisation spokesperson said.
"Despite the immediate efforts of hospital staff and emergency responders to provide assistance, the young man sadly died from his injuries.
"Our thoughts are with the young man's family and loved ones during this difficult time."
Opposition Leader Jess Wilson empathised with the victim's family and mum who had "woken up this morning to the worst possible news of her life".
"It's devastating to see the record levels of crime in this state now taking another young life," Ms Wilson told reporters.
She pledged to put more police on the beat and change laws so people faced consequences for their crimes should the opposition win the November state election.
"Victoria is broken. It is broken its very soul," Ms Wilson said.
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