The plane, an Airbus A320 belonging to flagship carrier Alitalia and flying in from Madrid, had 151 passengers on board, Italian news agency ANSA reported.
The report cited officials as saying there were around 10 "code green" light injuries among the passengers, who were treated by medical staff at the airport.
The pilot realised as he was coming in that the plane's right wheels had failed to deploy and he warned air traffic control ahead of time, the report said.
The plane then toppled on its right wing during landing and could be seen on its side near the runway, it added.
The national air transport safety agency said it had opened an investigation into the incident and dispatched two officers to examine the plane.
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