"The international break [next week] has led to the opportunity being taken to remove some metalwork from his arm," the club said on their website on Monday.
"That was left over from a bone break prior to the 2010 World Cup and he should be ready to rejoin training when his colleagues go away with their nations."
Drogba's fellow striker Nicolas Anelka is back in the squad for the game against Genk in Belgium after missing Saturday's embarrassing 5-3 home defeat by Arsenal through injury but midfielder John Obi Mikel is rested.
Manager Andre Villas-Boas denied media reports he gave his team a dressing down and ordered extra training the day after the Arsenal match.
"There was no kind of rant and no extra work -- it was a conversation between people," said the Portuguese. "It is not my leadership style to shout and my management is always two-way management.
"The players are encouraged to give their opinion because they are the ones that take their talent on to the pitch."
Saturday's defeat was the second in a row for Chelsea in the Premier League, after losing 1-0 at Queens Park Rangers the previous Sunday, and Villas-Boas acknowledged it had been a particularly difficult week.
"Our progress was stopped disastrously with two defeats in the league but it doesn't mean our philosophy is wrong and we are not on the right track," he said.
"It doesn't mean our castle fell down but we have to recover. There is no running away from our responsibilities... we know things are not right when you concede five goals at home and we have to address that."
Defender Branislav Ivanovic said the Chelsea players were still fuming about their performance against Arsenal.
"The whole team is angry and we have to show the reaction and our character, to change things," said the 27-year-old Serbian international. "It was a big derby and when you lose you cannot be happy.
"As a defender I can never be happy with conceding five goals. The good part is we know where we made mistakes and we can try everything to make sure it does not happen again.
"Words don't need to be [spoken]. Every one of us has to look in the mirror, to be honest with how we played defensively," added Ivanovic.
Chelsea are looking to do the 'double' over Genk after crushing the Belgians 5-0 at Stamford Bridge two weeks ago.
The Londoners are top of Group E with seven points from three games, one ahead of Bayer Leverkusen. Valencia are third with two points and Genk are bottom with one.
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