The Gunners boss has played down any hopes that the 24-year-old could feature in Brazil and has advised the winger to concentrate on recovering for the start of the next seasonArsenal boss Arsene Wenger has revealed that Theo Walcott's knee surgery went "very well" but insists it will be impossible for the England international to recover in time for the World Cup.
The 24-year-old winger suffered a cruciate ligament injury in the 2-0 win over Tottenham at the beginning of January, with the early prognosis suggesting that he would be out of action for six months.
Walcott has now gone under the knife in an attempt to cure the problem and Wenger has confirmed that the operation was successful, but promptly played down any hope that he could still play a part for England in Brazil.
"It went very well," the Gunners boss told reporters. "The damage was real in the knee so he will have to take the needed time, so let's not be hopeful that he will go to the World Cup - that is not possible.
"But, overall, his long-term future is very positive. It's about being fit for next season now."
Wenger also confirmed that Tomas Rosicky underwent surgery after suffering a broken nose in the 2-1 win over Aston Villa, while Mikel Arteta, Nicklas Bendtner, Aaron Ramsey and Thomas Vermaelen are all set to miss Saturday's meeting with Fulham.
"Rosicky had surgery with a general anaesthetic for a broken nose in two places. With a mask he may be available, but we have to monitor it closely," the Frenchman added.
"Ramsey and Arteta are both out for this game. Vermaelen, too. I personally believe the three will miss the Coventry game as well and will be available after that. Bendtner has a little chance to make Coventry. But in all probability it will be after that.
"Monreal looks a doubt for Saturday, a big doubt, because he twisted his foot on the kick. It is not the bruise, he turned and twisted the ligament."