The 18-year-old netted his first Barclays Premier League goals with a brace in the 7-1 trashing of 10-man Blackburn at Emirates Stadium on Saturday.
There are already calls for Oxlade-Chamberlain, a £10million signing from Southampton last summer, to be fast-tracked into the full England squad for the European Championship.
Wenger, though, has seen first hand how the overuse of midfielder Jack Wilshere - yet to play for Arsenal this season because of a stress fracture in his ankle - can result in problems further down the line and believes Oxlade-Chamberlain's progress must be closely monitored going forwards.
The Arsenal manager said: "That is what happened to us last year with Wilshere, it was exactly the same.
"At the start of the season you think: 'I will play him 20 games, maybe 25', but after they deliver a performance, they play 45 and then they play for the national team and then they get injured.
"It is very difficult to manage because people understand very quickly what kind of influence the players have and you want to win the game so you play them."
Wenger added: "I don't know where I have seen it, but 70% of the players who play very early in many, many games have stress fractures. In England the intensity of a game is higher."
Robin van Persie netted a hat-trick to help sink Rovers, his first coming after only 79 seconds.
The Dutchman believes Oxlade-Chamberlain has a "great future", but also warned against expecting too much too soon.
"Alex is a big prospect. Everyone is enjoying watching him, I do, you do and he brings something extra to the game and people just love it," said Van Persie.
"But don't put too much pressure on him. You always have periods when you are young when you have really high highs, then you go up and down until you balance it a bit better.
"He will have ups and will have periods when he is not playing so well, so my advice is to be aware of it and be patient."
England winger Theo Walcott set up Van Persie's opening two goals, and also laid on the pass for Oxlade-Chamberlain's second after a darting run through the Blackburn box.
The Gunners skipper "cannot understand the criticism" often directed towards the pacy forward.
"I love him, I honestly love him," Van Persie said.
"Theo was sharp, he was playing fantastically and, like anyone, he misses chances - but I miss chances. Ronaldo misses chances, Messi misses chances. It is life, you know.
"Sometimes I feel that people are a bit harsh on him. I don't know why. If you look at his assists rate then it is unbelievable.
"Theo will score. Trust me, he will score. He will get 20 goals at least every season. You will see. He will, trust me. Have faith in him."