In this specific case: Yes. I don't know much about the Irish province of Munster, but according to Wikipedia its Gaelic name is Cúige Mumhan, and I highly suspect that the English Munster is in this case a romanization of Mumhan by the Norman invaders.

The name of the German city of Münster however comes from her origin as a monasterium, a monastery. Münster is germanized latin. Actually the word Münster or the word component -münster is a pretty common toponym in Germany because of monasteries and minsters. -- Yes, you read quite right: Münster is also the German word for minster, a certain type of church. (Although, as far as I know, the English minster and the German Münster do not correlate precisely. But I'm no medievalist or ecclesiastical historian.)