The Polish goalkeeper was reported to have been found smoking in the showers following a 2-0 New Year's Day defeat to Southampton in the Premier League and was dropped for the 2-0 FA Cup win against Hull City.
But Wenger says he would prefer such matters to remain private.
"What happens in our dressing room stays in our dressing room, apart from the fact that it doesn’t," he joked.
It is as yet unclear whether Szczesny will return to the starting XI for this weekend's clash with Stoke City, but Wenger has backed the 24-year-old to bounce back from the indiscretion.
"I haven't selected the first XI yet," he added. "I take everything into account. I don't think it has been damaging but ideally you want everyone to behave in a perfect way.
"I like Wojciech as a person. When he makes a mistake he stands up for it.
"He has contributed as well to the good image of Arsenal Football Club. He is a guy who learns from his mistake. I am happy with his development.
"Yes, he did apologise. He is a serious boy who works very hard. He made a mistake. He is not the first one and not the last one.
"Every club has its own internal discipline or rules. It doesn’t need to be public.
"My issue is the player here is judged on their performances. Ideally to have a high level of performance is to behave as close as possible to the rules.
"I'm against smoking but have grown up in a period where, to accomplish military service, you are paid by cigarettes.
"You were encouraged. When I was a young boy, I was surrounded by smokers. I smoked myself when I stopped playing and was a young coach. I was only alerted later. We know now it's not good."
