The coast guard says rescue teams were called last evening after receiving a distress signal from the helicopter, operated by CHC, a company that transports people to and from offshore oil and gas platforms.
The agency said 15 people have been rescued from the sea and three others are missing after the incident, which took place near Sumburgh Airport.
Three helicopters and two lifeboats are searching the area for the missing people.
CHC said the aircraft was approaching Sumburgh Airport when it lost contact with air traffic control. It said there were 16 passengers and two crew members onboard.