The contractor, believed to be in his 50s, was injured at about 10.30am (3.30pm WST) while moving a mobile well servicing rig, the Jerusalem Post reported.
It quoted a spokesman from Engie subsidiary Afek as saying the man was injured while disassembling equipment.
The spokesman said Viking said his family had been notified of his death, and a team will be flown in to start a full investigation into the incident tomorrow.
Viking had been carrying out well testing on Ness-2, known as ‘Deborah's Well', after flow tests produced gas and small amounts of oil to surface.
Afek said last week that the latest testing would be carried out by its own scientific crew along with "external international experts" who are trying to find "sweet spots" of oil or gas reservoirs in the Golan Heights, which is claimed by both Israel and Syria.
While testing started on Ness-3 in February showed the well did not produce a level of hydrocarbons sufficient for commercial production, initial results from analyses "suggest that there may be a large reservoir of natural gas", along with "significant amounts" of light oil in the area.
Afek received a renewed permit on February 1 to continue exploring for conventional oil at up to 10 sites, despite opposition from environmental and political groups.
The company has completed five wells in the Golan Heights.