The Hughes 269C smashed into the Mentone home in the city's southeast about 1pm on Wednesday during a routine training course.
The man sustained injuries to his lower body and has been taken to The Alfred Hospital for further assessment.
He was trapped for about an hour before emergency services used a crane to free him from the wreckage.
No one was in the home at the time of the crash, with shaken neighbours reporting a loud bang when the aircraft hit the roof.
Surrounding roads will remain closed until authorities declare the scene safe.
Victorian Police Senior Sergeant Andrew Wise said it was too early to determine what caused the accident.
"I'm not too sure whether it was luck or unlucky, but we're thankful on this case that no one appeared to be too seriously injured," Snr Sgt Wise told reporters at the scene on Wednesday.
"His injuries are yet to be assessed but he is conversing with the ambulance members."
Neighbour Matt Evans raced home from work to check on the safety of his wife and baby, who were at home at the time.
"[My wife] heard a loud bang and then looked out the window and there was a helicopter on the roof," Mr Evans said.
There was slight damage to their property but no injuries.
The street is close to Moorabbin airport and Mr Evans said he had often worried about an aircraft crashing nearby.
It's understood the student, who trains with The Helicopter Group at the airport, was completing a solo NAV flight, which is required in order to obtain a pilot's licence.
Jesse Vanderzybb, whose father owns The Helicopter Group, said the accident had sparked strong emotions and brought back memories for his father.
"He's upset but everyone's alright ... he's been in the aviation industry for 35 years," Mr Vanderzybb said.
The Australian Transport Safety Bureau (ATSB) has launched an investigation into the crash.
"The helicopter was reported to have been conducting a missed approach (go-around) procedure from Moorabbin Airport when it collided with the roof of a house," the bureau said in a statement.
It said bureau investigators would interview the pilot and witnesses and review recorded data, weather and aircraft information and maintenance records before publishing a final report detailing contributing factors and any identified safety issues.
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