“There is no chance of the Euros for him,” said Wenger. “He will be back at the beginning of July.”
Oxlade-Chamberlain, who made his England debut against Norway in 2012, had been scheduled to feature for the Gunners’ Under-21 side earlier this week.
“He was out for a while and was not overloaded with games,” Wenger added.
“You want a guy of 22 years of age to go to the European Championship, so it is very sad.”
Oxlade-Chamberlain was a surprise call-up to Roy Hodgson’s squad for Euro 2012, becoming the third-youngest England player to feature at a major tournament when he started the 1-1 draw with France in Donetsk.
He was part of Hodgson’s 23-man World Cup squad in 2014, but did not feature after injuring a knee during England’s final warm-up game against Ecuador.
England will face Russia, Slovakia and Wales in Group B at Euro 2016, which begins on 10 June.
Liverpool will “take the opportunity” when they play holders Sevilla in the final of the Europa League on 18 May, says Reds manager Jurgen Klopp.
After losing the first leg of their semi-final 1-0 in Villarreal, Liverpool produced a dominant display at Anfield on Thursday to win 3-1 on aggregate.
“When you perform like we did then you want to have it all and that is what we will try,” said Klopp.
“We will go there and try to do everything for this wonderful club.”
The match – at St Jakob-Park in Basel, Switzerland – will be Liverpool’s first European final since losing 2-1 to AC Milan in the Champions League in 2007.
The Reds have won eight of the 11 European finals they have appeared in – five of seven in the European Cup/Champions League and three of three in the Uefa Cup/Europa League.
Should they beat Sevilla, who are trying to win the Europa League for the third successive season, they will join the Spanish side as the most successful in the competition with four victories and earn a place in next season’s Champions League.
“I don’t know what it means that it is nine years between Liverpool’s last final,” said Klopp, who replaced Brendan Rodgers as manager in October.
“A lot of teams want to go to finals, it is not too easy, but it is a real opportunity and we will take the opportunity.”
An early Bruno Soriano own goal set Liverpool on their way, before second-half strikes from Daniel Sturridge and Adam Lallana completed victory over their Spanish opponents, who finished the match with 10 men after Victor Ruiz was sent off.
‘100,000 Liverpool fans for the final’
Liverpool, Champions League winners in 2005, were backed by impressive support from the moment the team bus arrived at the stadium.
Hundreds of fans packed Anfield Road to welcome their players and continued their vociferous support throughout the game.
Klopp says as many as 100,000 Liverpool fans could travel to Switzerland for the final, though FC Basel’s stadium can only hold 38,000.
Klopp hails ‘unbelievable’ Sturridge
Klopp did not named a recognised striker in his starting line-up for the first leg, with Sturridge left on the bench.
However, he restored the England international to the first XI and was rewarded with an impressive performance.
Sturridge scored Liverpool’s second after being the closest Reds player to Soriano when he put through his own net – and he was also involved in Lallana’s goal.
Klopp said the 26-year-old had a “great game”, adding: “When Daniel Sturridge is fit he is an unbelievable striker, but even he needs players to play with and I know about his quality, I knew before I came here. Great player.”
Special times ahead for Liverpool?
Liverpool produced another memorable European performance at Anfield, after coming from 3-1 down to knock Borussia Dortmund out in the previous round.
It means Klopp is into his second final with the club since taking charge just seven months ago. They lost on penalties to Manchester City in the League Cup final in February.
“In 2016, the team have shown a lot of times what they could be capable of in the future so that’s a good sign and that is more important for me as a manager,” said Klopp.
Former Liverpool striker Michael Owen said on BT Sport: “Over the last few months we’ve really seen something special.
“There’s such high energy levels, the pressing we all knew Jurgen Klopp was going to bring over. But he’s just improving players – the likes of Adam Lallana, Simon Mignolet and Dejan Lovren – as well.
“There’s special times ahead. It’s almost like they are unbeatable here. It’s becoming a fortress.”