A search operation is continuing involving coastguard, police, RAF and local lifeboats following the incident at 6.20pm around two miles west of Sumburgh airport, on the southern tip of the main island.
The helicopter's life rafts were found empty and some wreckage from the aircraft has started to wash up at the southern end of Sumburgh, the coastguard said.
A spokeswoman said: "There were 18 people on board and 15 have been recovered, there is still an ongoing search and rescue mission for the three missing people."
The 15 injured have been taken to Gilbert Bain Hospital in Lerwick by coastguard helicopter.
A spokeswoman for the coastguard said passengers suffered a range of injuries.
She said: "The people that were involved are in varying stages of injury, no one has walked away from this without a scratch."
The stricken aircraft, operated by the company CHC, was taking workers to and from oil and gas platforms in the North Sea.
It was on its final approach to Sumburgh, with two crew and 16 oil workers on board, when it came down.
A company spokesman said: "CHC Helicopter can confirm that there has been an incident involving one of our aircraft in the North Sea, approximately two miles off Sumburgh.
"Exact details of the incident, which happened at approximately 6.20pm are not yet known.
"The appropriate authorities have been informed and the company's Incident Management Team is being mobilised."
Police Scotland said they were aware of the incident and were working with the coastguard.
A spokeswoman for Northlink ferries said at least one ferry and possibly two had been diverted to help with the rescue.
"The Coastguard are in the lead of the operation, but I can confirm that at least one of our ferries is providing assistance," she said. "There will definitely have been passengers aboard that ferry."
The ferry is believed to have been travelling between Shetland and Orkney and is thought to have been carrying up to 100 passengers.
Investigators from the Air Accidents Investigation Branch (AAIB) were travelling to the scene this evening.
A spokesman for the Department for Transport said: "The AAIB is aware of the incident and has deployed a team".
Last year, two helicopters ditched in the North Sea only six months apart. All passengers and crew were rescued in both incidents which were found to be caused by gearbox problems.
In October, 17 passengers and two crew were rescued from life rafts by a passing vessel after the helicopter, which was carrying an oil crew from Aberdeen to a rig 86 miles north west of Shetland, was forced to ditch.
Previously, in May 2012 all 14 passengers and crew members on a Super Puma helicopter were rescued after it ditched about 30 miles off the coast of Aberdeen. The helicopter was on a scheduled flight from Aberdeen Airport to a platform in the North Sea at the time.
Super Puma EC 225s were grounded in the wake of the two incidents but were given approval to fly again and services resumed earlier this month.
In April 2009, 16 people died when a Super Puma plunged into the sea. Its gearbox failed while carrying the men to Aberdeen. The Bond-operated aircraft was returning from the BP Miller platform when it went down off the Aberdeenshire coast on April 1, 2009.