Gervinho is suffering with a mild muscular problem and Koscielny has damaged his ankle, while Walcott limped off during Saturday's victory over Bolton with what was later described as a minor knee injury.
All three players remain in contention for Sunday's derby clash with Tottenham at White Hart Lane, but they have been ruled out of Wednesday's game at the Emirates.
The recent news that Wilshere will miss the rest of the year due to surgery is a particularly big blow, but Arsene Wenger was at least pleased that the midfielder's ankle operation went well.
"It was a big relief that Jack's operation went well," Wenger said. "Our medical staff did not make any mistakes. It's very difficult to predict how long he will be out, but at least four months for certain. It has changed because the fracture he had didn't heal, so we had to move quite quickly.
"He had an early fracture at the age of 16 that healed, and around that it created another opening. Is it down to a kick? Is it down to playing too much? I'm not a specialist. I don't know what kind of impact it has. It makes us a bit short in midfield and puts more pressure on our midfielders to perform game in, game out."
It has been a difficult start to the season for Wenger, and his mood would not have been helped at the weekend when Robin van Persie - who has less than two years remaining on his contract - was quoting as saying he may defer talks on an extension.
"It depends on us, on him," Wenger said. "On our side we are quite clear, so it is no problem. It doesn't depend only on us - we are clear on our intention. After that we have to respect. There is nearly two years to go, so let's not make an issue of something like that - two years in football is a very, very long time."
He added: "I had a high level of expectation for him. He does as well as I expect, he plays well with the team and his finishing record is absolutely fantastic: 26 goals in 31 games - and he is not only a finisher."