Queens Park Rangers defender Rio Ferdinand was this week banned for three matches and fined £25,000 by the Football Association for comments he made on the social network.
And Wenger says it is difficult to keep certain issues under wraps following the explosion in social media use over the last few years.
“We are concerned as well about statements on Twitter, things going out of the club that should not go out,” Wenger said.
“It’s important to keep that under control. In the modern world, it’s very difficult but we try.”
Arsenal host Burnley in the Premier League on Saturday afternoon.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news