TAQA, three-quarter owned by the government, said it made a profit of $113m (£71m) on the sale.
Tesla was founded in 2003 and its best car is the 2008 Tesla Roadster, which is sold in 32 countries.
The company, which also has part shares owned by carmakers Daimler and Toyota, has seen its 2010 share listing price of $10 double since then.
Tesla expects to become profitable in 2013 and envisages a tripling of revenues this, helped by July deliveries of its premium electric car, the Model S.
Abu Dhabi’s TAQA said it had sold the 7.3 million shares transferred to it by the Abu Dhabi Water and Electricity Authority in late 2010.
It said it had “admiration for Tesla’s vision, technology and products”, but that the carmaker was a non-core investment for the body.
The emirate remains the largest shareholder in Daimler through its sovereign wealth fund Aabar Investments.
Source; BBC NEWs