Oxlade-Chamberlain scored in Monday's pre-season 3-1 win over Mexican club Guadalajara Chivas in California.
Oxlade-Chamberlain, who damaged his knee in a Champions League match against Barcelona in February, scored in Monday's pre-season 3-1 win over Mexican club Guadalajara Chivas in California.
Arsenal begin their new season with crucial games against Liverpool at the Emirates on Aug. 14 and a trip to Premier League champions Leicester City six days later.
"It's a very important season for him. He has been out for a long, long time. He has been injured and did not go to the European Championship. That's why I'm cautious with him," Wenger told the club's website.
"I hope I can get him through and fit for the start of the season. (He gives us) power, penetration. It's difficult what he doesn't have... that's why I would like him to get to the level he can go to."
Wenger is also optimistic Spanish midfielder Santi Cazorla can regain fitness by the end of August after a long injury layoff last season due to a knee injury.
"He is our technical security in midfield and we missed him for five or six months last season. At the moment he is not completely there on the fitness front," Wenger added.
"He's a bit behind the others physically but I think he will be alright, maybe not on August 15th, but at the end of August he should be alright."