The driver was taken to the town’s Gilbert Bain Hospital with suspected broken ribs.
The Shetland News reported that the accident happened when steel beams were being moved before assembly at the site of the council’s new social work headquarters, at the North Ness Business Park.
The £6m project is being built by local construction firm Hunter & Morrison and financed by SLAP, the property arm of the Shetland Charitable Trust.
Trust financial controller Jeff Goddard said the Health and Safety Executive had been informed and an investigation to find out what exactly went wrong had been launched.
It was reported that the driver half fell and half jumped from the cab when his mobile crane started to topple.
He managed to escape by rolling under a trailer before the crane crashed down upon it.
The steel beam the crane had been carrying hit the ground and fell over onto the crane.
Goddards said: “It was a small mobile crane that fell over and the beam that it was carrying came down on top of the crane.
“As far as we can tell, the man fell out of his cabin and rolled under the lorry itself.
“We take safety obligations very seriously. As it happens we had a site visit there this morning, where all the health and safety people confirmed they were happy that this was a very well run site.
“As far as we can tell, it was an unfortunate accident. There is no suggestion that procedures had not been followed.
“It shows that building sites need to be treated with respect and that things can go wrong.”