The company operated a retail outlet in Edinburgh as well as supplying retail customers across the UK.
Administrator Ernst & Young blamed the recession, competition from supermarkets and falling orders from corporate clients for its demise.
Five of its seven staff have been laid off. Joint administrator Colin Dempster said: ďThe group has been impacted by the recent economic downturn, which has unfortunately led to a declining order book and the directors concluded that the business can no longer continue to trade.
ďWe are actively marketing the business for sale and are keen to hear from any interested parties,Ē he said.
E&Y is seeking a buyer for the companyís stock and name, and said there had been a ďgood level of interestĒ.
The company was owned by Ian Macphail, part of a management buyout team that took the company out of a previous administration in 2004.
He bought out business partner David Forbes in 2006.
Macphail began his career as a cellar boy with Cockburnís before going on to manage a Bottoms Up, returning to Cockburnís in 2002 as wine director.
Cockburnís claimed to be Scotlandís oldest wine merchant, founded by Robert Cockburn in 1796. His brother was the founder of Cockburnís port.
Famous customers have included Sir Walter Scott and Charles Dickens.
The desk at which Scott placed an order for 350 cases of wine and 36 cases of spirits is still in use as a talking point for customers at the Edinburgh shop.
The company accounts for the year to May 2008, lodged at Companies House, show a loss of £196,169, although this was down on £221,161 from a year earlier.
The demise of Cockburnís adds a prestigious name to the list of off-trade casualties of the recession.