Team spokesman Eric Kacou said Monday it's not known when Drogba can resume training after the squad arrives in South Africa on Thursday, or if he will play at the World Cup.
Surgeons operated on Drogba in the Swiss capital Bern on Saturday.
The 32-year-old forward was injured in a collision with Japan defender Marcus Tulio Tanaka early in Ivory Coast's 2-0 victory in a warmup match last Friday.
Ivory Coast coach Sven-Goran Eriksson has said he's hopeful Drogba can still play a part in the tournament.
Ivory Coast completes its Group H schedule against Brazil in Johannesburg, on June 20 and North Korea five days later in Nelspruit.
Drogba will be on the bench backing his teammates when they play Swiss second-division club Lausanne Sports at Nyon on Tuesday, Kacou said.