Helicopter operator CHC said it has grounded the AS332 L2 aircraft which ditched without warning while carrying 18 workers on Friday evening.
The company has also suspended all UK commercial flights of three other Super Puma models following a recommendation from an aviation safety association.
The offshore industry's Helicopter Safety Steering Group (HSSG) urged the precautionary measure until there is "sufficient factual information" to resume flights.
Rescuers are yet to recover one of the bodies from the site of the crash around two miles west of Sumburgh airport. The cause of the accident is not yet known.
Those who died have been named as Duncan Munro, 46, from Bishop Auckland, County Durham; George Allison, 57, from Winchester, Hampshire; Sarah Darnley, 45, from Elgin in the Highlands and 59-year-old Gary McCrossan, from Inverness.
The helicopter was being operated by CHC for oil company Total and was transporting workers from the Borgsten Dolphin platform when it is believed to have experienced a "catastrophic" loss of power as it approached the airport on the southern tip of Shetland's main island.
The HSSG is made up of representatives from oil and gas firms, contractors, helicopter operators, offshore unions, the Health and Safety Executive (HSE) and the Civil Aviation Authority (CAA).
The group met in Aberdeen yesterday and recommended the temporary suspension of all Super Puma commercial passenger flights to and from the UK's oil and gas installations.
This includes the AS332 L, L1, L2 and EC225 models.
CHC said it was "devastated" by the accident and would follow the recommendation, which allows for the operation of emergency rescue flights.
Fellow operators Bond Offshore Helicopters and Bristow have also enforced a temporary suspension of Super Puma flights.
Bristow said three flights scheduled for today had been cancelled and further updates would be issued in due course.
The HSSG will meet again on Wednesday to review the suspension unless "any significant information come to light before this date".
Industry body Oil & Gas UK has meanwhile arranged a meeting of operators and major contractors tomorrow to discuss ways of minimising the impact of the grounding of flights on the offshore workforce.
Scotland's Finance Secretary John Swinney said the government did not anticipate that the temporary suspension would have any immediate impact on the production of oil and gas in the North Sea but that the situation would be closely monitored.
"My thoughts are with the families, friends and colleagues of those who lost their lives and I hope those who were injured make a good recovery," he said.
Of the 14 survivors, two remain in hospital on Shetland and 12 returned to Aberdeen yesterday.
One Total employee was on board and the remainder worked for contract companies, including those killed.
Mr Munro leaves behind wife Penny and 12-year-old daughter Katie.
His family said in a statement: "He will be sadly missed by everyone that knew him and his death will leave a large void in a lot of people's lives."
Ms Darnley's family paid tribute to a ''fun-loving, free spirit'' who was brought up in Elgin and moved to Aberdeen aged 19.
The offshore worker is survived by parents Anne and Edmund Darnley, her sister Angela and nephew Nicholas.
Her mother Anne said: ''We are shocked by the sudden loss of Sarah, who was a fun-loving free spirit who will be sorely missed.
''Sarah lived life to the full, she was easy going and a one-off. She will be deeply missed by all who knew her.''
Mr McCrossan worked for Stork Technical Services. Mike Mann, a senior vice president at the firm, said: "Our heartfelt condolences go out to Gary's family and to all of those affected by this tragedy."
Mr Allison had been working at the Offshore Dunbar Platform as a project safety supervisor for just over a year when he was killed, according to his LinkedIn profile.
He described himself as a "highly qualified, experienced and competent Safety Advisor" who has worked in the offshore industry for 27 years.
A team from the Air Accidents Investigation Branch has travelled to Aberdeen to carry out initial inquiries into the incident.
There have been five North Sea incidents involving Super Pumas since 2009. In April that year an AS332 L2, this time operated by Bond, went down north east of Peterhead on its return from a BP Platform, killing all 14 passengers and two crew on board.
Pat Rafferty, Scottish secretary of the Unite union, said: ''This is the fifth major incident in the last four years involving Super Puma helicopters in the UK offshore industry and the second resulting in fatalities. It's unacceptable and it can't go on."
Super Puma manufacturers Eurocopter said the company was "supporting CHC and relevant authorities with their investigations".
A Bond spokesman said: "At this time, and until further information becomes available, Bond Offshore Helicopters will not be operating any of its Super Puma aircraft fleet, with the exception of our Jigsaw rescue aircraft which will be available for life-at-risk missions.
"All other flight operations continue as scheduled."
Volunteer lifeboat crews from Aith and Lerwick yesterday assisted coastguard in their attempt to recover the remaining body at sea and collect debris from the crash site.
The RNLI said it had not been possible to recover the remains from the wreckage during the operation and the crews were last night stood down.
A spokesman said: "I don't anticipate we will be involved any further, but obviously we were happy to assist as much as we could.
"One cannot imagine the turmoil that families and loved ones of those who died must be going through, and they are at the forefront of our minds at this very distressing time."
Representatives from the oil and gas industry have set up a fundraising page in aid of the RNLI following its rescue effort on Friday.
Shetland coastguard manager John Webster said: "There is one person still unaccounted for. That search is ongoing and we will hopefully have it resolved in the next few hours.
"The heavy-lift ship is out at the moment trying to recover what wreckage it can from the sea.
"After that the Air Accidents Investigation Branch will decide where to take it. I suspect it will be to Aberdeen first then on to wherever they do the investigations.
"A lot of our crew are shocked, to say the least. The majority are holding out well but one or two are suffering a wee bit more than others.
"Our role will end as soon as the final body is recovered."
He added: "We've dealt with a few air crashes before. Each one is different but each is as sad as the last."
Mr Webster said of the moment he was alerted to the crash: "We got a call from the ARCC (Aeronautical Rescue Coordination Centre) to say that an inbound helibus had disappeared off the radar.
"That was the first indication that we had that something serious had happened, and we mobilised our helicopters, ground teams and lifeboats to the last known position.
"Of course when the units got near the position they saw the wreckage of the helicopter, which was actually upside down at the time."