The German side are strong favourites to progress in their last-16 tie, but Arsenal's Polish keeper doesn't believe that status is entirely justified.
"I don't know why they should be favourites," he told the official Arsenal website. "I wouldn't bet money on this one.
"I really wanted to avoid Barcelona. I would take any other team because I believe Barca are the best in the world. You want to avoid them because your chances are very small of beating them. Bayern is a very tough draw but it is a very exciting one.
"Bayern are flying in the Bundesliga. They have fantastic individual players like [Arjen] Robben, [Franck] Ribery and [Manuel] Neuer in goal. They are very strong but we won't be scared."
Szczesny placed plenty of emphasis on getting a result in the first-leg at the Emirates on Tuesday evening.
"Ideally you would like to play the first leg away but we may get a decent advantage like AC Milan did," he said. "Hopefully, we can take a lead to their place, because it will be very tough at the Allianz Arena.
"Arsenal supporters are always fantastic, especially on Champions League nights. It is always a bit more exciting and if we can match the atmosphere with the performance then we will have a good chance of getting a result."
Cmon guys 'Positive Mental Energy'. We can be negative all we like afterwards. We are the Arsenal. C'mon you Gunners.- gunnergremlin