The 49-year-old had been working on the Noble Lloyd Noble installation, in the Mariner Field, approximately 90 miles (150km) east of Shetland.
The alarm was raised at about 21:20 on Tuesday after a search of the rig failed to locate him.
A search and rescue helicopter, two standby vessels and a platform supply vessel are involved in the search.
Insp Steve McEwan said: "An extensive search of the rig itself and the water surrounding it is ongoing, led by the Maritime and Coastguard Agency (MCA).
"This involves the use of a search and rescue helicopter, two standby vessels and a platform supply vessel.
"We are working closely with the companies involved and next of kin to keep them informed of any developments."
Noble Lloyd Noble is one of the world's largest jack-up rigs, an installation with long support legs that can be lowered to the sea floor.
The operator Statoil is developing the Mariner field with the first oil expected in 2018.
Source: www.bbc.com (Last Updated: 7:15 AM, 10-May-2017)