The plane that crashed in Merebank south of Durban on Thursday had declared an emergency shortly after take-off, carrier Airlink said.
"The aircraft, a Jetstream 41 (29 seats), departed from Durban International Airport and shortly after take-off declared an emergency, crew reported engine loss and smoke from the rear of the aircraft," said a statement posted on their website.
"The aircraft ditched approx 400 m off the airport in the fields of the Merebank high school on the Bluff and broke into three pieces on impact."
The crash occurred after take-off at around 8am while they were en route to Pietermaritzburg.
The two pilots sustained critical injuries but were stable.
The flight attendant was seriously injured but also stable.
The captain was airlifted to St Augustine hospital at 11am and the crew members were taken to nearby hospitals.
A person on the ground was slightly injured and was treated at the scene and admitted to hospital for surveillance.
There were no passengers on board.
Arrangements had been made for the immediate family of the injured crew to travel to Durban.
KwaZulu-Natal's transport MEC Willies Mchunu called on aviation authorities to probe the case of the crash.
"We can least afford to have passenger airlines jeopardising the lives of our people. Due to the risk associated with air travel, its safety must be beyond reproach," a statement from his office said.
Earlier, Transport Minister Sibusiso Ndebele sent wishes of a speedy recovery to those injured in the crash.
"We want to wish those injured in the plane crash in Merebank this morning a speedy recovery," said Ndebele.
"We acknowledge that this is a difficult time for those injured and their families and our thoughts and prayers are with them," his statement continued.
Accident investigators from the Civil Aviation Authority were sent to the scene and an on-site investigation will be carried out from which a report will be prepared to determine the probable cause of the crash.
A Sapa reporter on the scene said paramedics used jaws of life to cut the people free from the plane which broke up after crashing into a fence.
Initially it was thought that only those on board the plane were injured, but it later emerged that a woman who had been on the school's perimeter was also injured.
Abel Pillay, whose house is a stone's throw from the crash scene, said he saw the plane flying very low and it looked as though the pilot was trying to land on the sports ground.
"My father said 'look at the plane, it is flying very low'," Pillay told Sapa.
"You could see that the pilot was trying to land in the school ground."
Pillay said there were three people cleaning the street and that one was hit by the plane and fell, but survived.
The plane narrowly missed crashing into houses.
A large group of residents arrived to observe the rescue operation from behind a cordon that had been set up. - Sapa