Oxlade-Chamberlain, 18, scored twice for Arsenal as they routed ten-man Blackburn, who had Gael Givet sent off in the first half, to earn their first league win in five matches.
Of his performance, Wenger, who signed the midfielder from Southampton for £12 million last summer, said: "Three months ago he was not ready, in my opinion.
"He had shown talent, but suddenly in the last two or three months he has stepped up. You can see that in every game he becomes more important and his personality comes out in the game."
Wenger also expressed his delight at the three points, suggesting that he felt a success had been coming following a run of disappointing results which saw them off the pace in the race for fourth.
"We had a crisis of results for a while, but the way we played was never really bad," he told Sky Sports. "We had some good games and lost, but in the last week we played well against Villa and at Bolton.
"We played well today and overall it is encouraging. We had a comfortable day today and got the three points that we needed. The big question mark was how well had we recovered physically after putting in a lot against Villa and Bolton.
"We finished a bit tired at Bolton but today we started strong. When it was 11 against ten we were comfortable in a dominant way."