His country remain confident of a speedy recovery, and a spokesman said yesterday the 32-year-old could even feature in their first game against Portugal on June 15.
'He's not at all out of the World Cup,' he said.
But Drogba's injury is still a blow to manager Sven Goran Eriksson's hopes of qualifying from Group G, which also has Brazil and North Korea.
Fitness race: Didier Drogba broke his shoulder against Japan
The Chelsea striker went off holding his right arm after 17 minutes of the warm-up game against Japan on Friday. His operation was said to be a success but they did not know how long he would be out.
Drogba has scored 44 goals in 69 internationals and hit 37 for Chelsea last season as they won an FA Cup and League double.
Drogba set to miss finals after breaking elbow in Ivory Coast win over JapanGROUP G LOWDOWN: Brazil, Ivory Coast, North Korea and PortugalWORLD CUP 2010: Spotlight on the referees, the ones players and fans love to hate.CHELSEA FC