According to the official Emirates News Agency reported on Tuesday, the emirate's decision stems from its desire to focus it attention on its own airline, Etihad.
The move leaves Gulf states Bahrain and Oman as the remaining two stockholders.
Abu Dhabi launched Etihad last year, adding to tough competition for Gulf Air from established regional rival Emirates, owned by Dubai, the commercial hub of the region and second largest emirate in the UAE.
Oman also owns another national airline, Oman Air.
In the last financial year, Gulf Air turned a slim profit - the first since 1997 - thanks to a restructuring programme launched by Australian airline executive James Hogan in 2002.
Rising fuel costs caused by high oil prices increased the firm's operational losses in 2004, but Gulf Air offset this burden with a steep rise in non-operating income from sales of property and equipment.
Qatar, home to fast-growing Qatar Airways, pulled out of the Manama, Bahrain-based Gulf Air in 2002.