As investigations into the cause of the crash got under way, operator CHC Helicopter said the aircraft lost communication as it approached the airport on the southern tip of the main island.
It has suspended operations of the Super Puma AS332L2 until the cause of the crash is known.
The same model was involved in a North Sea crash in April 2009, off the coast of Peterhead, which killed all 14 passengers and two crew on board. Its gearbox failed while carrying the men to Aberdeen.
Friday's crash brings the number of major North Sea incidents involving a Super Puma to five since 2009.
The RMT union said the entire Super Puma fleet should remain grounded until the cause of the latest incident is established.
The four oil workers died on Friday after the AS332L2 helicopter crashed on Friday near Sumburgh Airport in Shetland with 18 people on board, including two crew.
It is believed a catastrophic loss of power led the Super Puma to plunge into the sea, forcing those on board to scramble out of side windows after the helicopter rolled over in the water.
Oil company Total, which runs the Borgsten Dolphin platform from which the four were returning home, said all the dead had been employed by contractors which supported the oil production process.
The RMT said it wanted every Super Puma craft to remain grounded until investigations concluded and Eurocopter, which builds the helicopters, could guarantee their safety.
A different Super Puma model - the EC225 - was involved in two incidents in the North Sea last year, and one in 2009.
In May 2012, all 14 people on board a Super Puma EC225 were rescued when it came down about 30 miles off Aberdeen during a flight to an oil rig. Then, in October, all 19 people on board another EC225 were rescued safely after it put down in the sea off Shetland. The incident was caused by a cracked shaft in the main gearbox.
In February 2009, a Super Puma EC225 ditched in fog a short distance from a BP oil platform in the ETAP field, 125 miles east of Aberdeen. All 18 people on board survived. Crew error and a faulty alert system were blamed.
Reacting to Friday's incident, RMT general secretary Bob Crow said: "Workforce confidence in the Super Puma type aircraft was severely dented after the two ditching events of last year and the fatal accident in 2009.
"RMT and Unite have worked with all sectors of the industry to address the concerns of our members and rebuild that confidence.
"Last night's events have undone all of that work and we anticipate an outpouring of anger."
Oil workers used social media to complain about safety standards on helicopters. One page, Destroy The Super Pumas, had nearly 5000 supporters last night.
Crow added: "The entire Super Puma fleet must remain grounded until the causes of this latest event are established and dealt with thoroughly to the union's satisfaction, and we will support any member who refuses to board any suspect aircraft type in light of this disaster."
The Helicopter Safety Steering Group (HSSG) also called for all Super Pumas to be grounded. HSSG said while there were "significant technical differences" between the variants, a cautious approach was needed. It said the grounding should include four models: the AS332L, L1, L2 and EC225.
Pat Rafferty, Scottish secretary of the Unite union, said the number of incidents involving Super Puma helicopters in the offshore industry in recent years was "unacceptable".
He said: "No-one should ever go to work and not come back safely to their family and friends."
Mark Abbey, from CHC Helicopter, expressed "heartfelt sympathies" to those involved in the crash and said all flights in and out of Aberdeen were halted as a mark of respect.
He said the company would not speculate on the cause of the crash.
Abbey added: "We are proud of our partnership with the industry and, like all helicopter operators, we have advanced considerably in terms of technology and predictability and the safeguards we put in place to mitigate risk.
"However, in a tragedy like this, none of that matters. What does matter is that while it is not possible to take all of the risk out of this industry it is our obligation to mitigate those risks and be as safe as we possibly can be."
Another operator, Bond Offshore Helicopters, has also halted operations of its Super Puma fleet.
Eurocopter, which builds the craft, is part of the European Aeronautic Defence and Space Company.
The EC225 models were temporarily grounded following the 2012 incidents and operator CHC returned the model to commercial service only earlier this month.
An Air Accidents Investigation Branch probe found two incidents were caused by gearbox failure and new advice on checks for the EC225 was issued. A fatal accident inquiry is due to be held in October into the AS332L2 crash in 2009.
Following Friday's accident, boats joined lifeboat crews from Lerwick and Aith and helicopters from the Coastguard, RAF Lossiemouth and two Bond rescue helicopters to search for survivors.
Fourteen people were taken to the Gilbert Bain Hospital in Lerwick, Shetland, including the two crew. Five were discharged and nine were detained overnight for observation.
The ditched helicopter was found broken into several pieces.