The 23-year-old former IRB player of the year had the operation to correct what doctors described as a "cervical neck injury with nerve root compression" which he sustained in last weekend's Test match against Scotland.
Burger has had a titanium plate inserted into his neck and is expected to be sidelined for between six and eight months.
The forward is now focused on getting back to playing in plenty of time for the World Cup in France next September.
"I am happy the operation was successful," Burger told South Africa Rugby's official website, www.sarugby.net,
"I will be following medical recovery and rehabilitation instructions carefully and am already focusing mentally on maximising each and every opportunity to ensure optimal recovery and a return to the game I love."
Burger did not realise he had been injured until several hours after the game.