It had originally been expected that the property, at the corner of Rathdowne and Queensberry streets, would fetch about $3.5 million when it was put on the market last month.
CB Richard Ellis agent Walter Occhiuto, who sold the property, said the level of demand by residential developers exceeded expectation.
Piccolo Developments is planning to develop luxury residential apartments on the 1746 sq m site.
"The site boasts proximity (to the CBD) and is opposite the Carlton Gardens and Royal Exhibition Building and Melbourne Museum," said Piccolo Developments director Michael Piccolo.
Piccolo recently developed the Cento apartments at 100 Queensberry Street into a 35-unit development, in a project worth more than $15 million.