Assuming you have the trip on one ticket:
If the airline sold you such a ticket, there is enough time - otherwise they wouldn't sell it.
Anyway, an hour is easy to do in Munich. Worst case, if you miss your connection, you get a free rebooking on the next plane - and there are many to Vienna.
Your bags are checked through; german customs doesn't care about them.
Outside of the USA, basically all airports are 'international', so only the final arrival needs customs to inspect your bags. Only in the USA exists the concept of 'non-international' airports, so you are forced to immigrate and pass customs on the first ('international') arrival - your connection could be to Cornfield, IO, which might not have customs and immigration.