However, the Ivory Coast Federation (FIF) remain confident of a speedy recovery.
The Chelsea star was forced out of the Ivorians' World Cup warm-up game against Japan in Sion yesterday in the 17th minute, leaving the field clutching his right arm.
The FIF have announced that today's operation was "a success" but have not yet confirmed how long the forward is likely to be sidelined for.
"Following the fracture of the ulna which Didier Drogba suffered in the international friendly between Japan and the Ivory Coast, on June 4 in Sion, the national team captain was today, Saturday June 5, admitted to the Lindenhof hospital in Berne," read a statement on the FIF website.
"He was taken care of by Professors Ralph Hertel and Michel Gaillot, eminent specialists in their area," the staement continued.
"The surgical operation which was necessitated by his condition was performed with success.
"Professors Hertel and Gaillot, as well as the Elephants' medical staff, are confident regarding the speedy recovery of the player.
"The FIF thank the sporting world and all those in the Ivory Coast, in Africa and throughout the world who have shown their support to Didier Drogba and the Ivory Coast."
The federation have not yet ruled Drogba out of the World Cup and yesterday a spokesman told Press Association Sport that the 32-year-old could even feature when they kick off their World Cup campaign against Portugal in 10 days' time.
"He's not at all out of the World Cup," he said. "He can still play.
"We don't know if he will be able to play the first game - that depends on the verdict of the medical team.
"But he's definitely not out [of the tournament]."
It is nevertheless a devastating blow to Ivory Coast's hopes of qualifying from Group G which, in addition to Portugal, also contains Brazil and North Korea.
Drogba has scored 44 goals in 69 appearances for his country and hit 37 for Chelsea in all competitions as Carlo Ancelotti's men landed the Barclays Premier League and FA Cup double last season.
Ivory Coast coach Sven Goran Eriksson said after the game: "It's an elbow injury for sure. How bad it is, I don't know. He had a lot of pain.
"Of course I am worried, he's our captain and one of the best players in the world."