"Theo is handling it as well as you can when you have had such a shock because he's mentally strong, he's very balanced as a person and he can put it into perspective," Wenger told the club website.
"We know that he will have the dedication and the serious attitude to come back as strong as ever."
The Arsenal and England forward is out for six months after he ruptured the anterior cruciate ligament in his left knee in Saturday's FA Cup third-round win over north London neighbours Tottenham Hotspur.
While Wenger is disappointed to lose the 24-year-old, he is confident he will make a full recovery. He said he felt Walcott was getting back to his very best at the time of his injury.
"We lost a very talented player, a very intelligent player and a player who was just grabbing his form again," he said.
"From game to game he became more influential, you've seen a complete player. He can always decide a game through a final ball or through a goal.
"Sometimes in the same game he does both. I felt against Tottenham he had a very convincing performance because he integrates well into our style of play as he's been here for so many years now," said Wenger.
"When we combine at a high pace he's involved in it because he understands exactly what we want to do."
Wenger admitted that Walcott's injury has "accelerated" his plans in the January transfer window.
But he emphasised that the Tottenham game showed he still had options already at his disposal.
"[Walcott's injury] has accelerated speculation first and of course my desire as well - but let's not forget about Serge Gnabry who can play in the first team," said Wenger.
"We have (Alex) Oxlade-Chamberlain back and we have many other players who can play on the flanks so to find better solutions than what we have internally will not be easy.
"Up front we lose Theo as a potential central forward and that's maybe where we have to look outside. But we hopefully have (Nicklas) Bendtner back in three weeks. We are there for the opportunities but it's very difficult at the moment."
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