Benteke ruptured his Achilles tendon in training last Thursday, and has returned to his home in Belgium for the operation.
Manager Paul Lambert said: "Our doctor (Roddy Macdonald) is over in Belgium and he has spoken with the surgeon, and it's pretty imminent he will get it done - today, tonight or tomorrow.
"Then after that it's all about the rehabilitation with him. When it's a long-term injury you have good days, bad days, like everyone else when they are out injured for a long time, but he'll be fine."
With Benteke out of the World Cup, and unlikely to return to match action until October at the earliest, the short-term shock will affect him.
Lambert believes, however, knowing the player as he does he will be eager to return as quickly as possible, not just for club, but also for country and qualification for the next European Championship.
"It's probably just sinking in now he is going to miss the World Cup, which is a major blow for him," added Lambert.
"But he is in a generation of Belgian players who will qualify for a few more tournaments down the line.
"He is still a young guy in that group, and he will come back totally strong, given the way he is as a guy and his physical aspect.
"Of course, everybody is different as to how they want to progress, and how quick their body heals.
"But looking at Christian and the way he is as a pro he will knuckle down and work really hard to get back.
"I've been told the surgeon is really highly regarded, so as long as the job is done right and everything goes swimmingly then he will be okay."
Ahead of Saturday's Barclays Premier League trip to Crystal Palace, Lambert will at least have three other key players available who sat out the 2-1 loss at home to Fulham last weekend.
Striker Gabby Agbonlahor and midfielders Fabian Delph and Karim El Ahmadi should all go straight back into the starting line-up for the game at Selhurst Park.
Lambert said: "They all trained this week and they're all fine."
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