The four-seat, twin-engined Diamond DA42 aircraft had just taken off from Parafield Airport, north of Adelaide, shortly after 2pm, when it crashed into a hangar where a significant amount of fuel was stored.
In a briefing at the airport, Chief Inspector Andrew McCracken said the two people who died were in the aircraft and four people had been rushed to Royal Adelaide Hospital.
"We have one in a life-threatening condition with serious and significant burns, two in a serious condition, and one with minor injuries," he said.
Another four people were being treated for smoke inhalation at the Lyell McEwin Hospital, and another two people were rushed to Modbury Hospital, also for treatment for smoke inhalation.
Metropolitan Fire Service Chief Officer Jeff Swann said on arrival, firefighters were faced with "really thick, black smoke, and intense flames".
"These flames were further intensified by a significant amount of fuel inside the hangar, and also the fact that the aircraft had impacted the fire hydrant system," he said.
This had knocked out the sprinkler system and also created a lack of water for the 57 firefighters who responded.
There were a number of students inside that were assisted out of the building by MFS.
The hangar had sustained significant damage, including to two of the five aircraft that were inside.
It was used for maintenance, aircraft storage and included a classroom space.
Chief Insp McCracken said he would not speculate on whether the pilot was a student "until I've had further confirmation from the investigations team and we've clarified and validated that information".
A forensic pathologist was at the scene, along with major crash officers, and a cordon would remain in place for least 24 hours while investigations continued, he said.
The Australian Transport Safety Bureau said a team of transport safety investigators from Canberra and Brisbane would arrive at the scene on Thursday morning.
They would undertake site and wreckage examination and recover aircraft components for examination at the ATSB's technical facilities in Canberra.
The area has been evacuated and authorities have asked the public to avoid the area around the airport.
Premier Peter Malinauskas said he had been briefed by Police Commissioner Grant Stevens on the "tragic incident".
"My thoughts are with the families and loved ones of those who have passed away, and with everyone affected by this devastating event," he said.
"I want to sincerely thank our first responders, including South Australia Police, SA Ambulance and Metropolitan Fire Service, for their swift and courageous response under very difficult circumstances."
