Chelsea will use the striker's domestic suspension as an opportunity to go ahead with the procedure.
He is out of Tuesday's trip to Genk but should return for the Premier League game against Liverpool on 20 November.
"[Drogba] should be ready for the team when the others go away for international fixtures," said manager Andre Villas-Boas.
The Blues' next domestic match is against Blackburn on 5 November, but the Ivory Coast player is ineligible for that fixture after he was sent off against Queens Park Rangers on 23 October.
Villas-Boas added: "We took the risk based on his domestic suspension and the forthcoming international break to remove six of the eight screws from his arm."
Drogba fractured a bone close to his elbow in 2010, initially putting his World Cup place in doubt, but successful surgery enabled him to play in a cast.
Drogba has scored only once in seven Premier League appearances this season and is yet to feature in the Champions League this term.