It would be highly unusual for a major theologian of that (or any) erra (and certainly for any of the Protestant reformers) to not have at least some familiarity with the source languages of the texts they studied and taught from. Also, Latin is pretty much a given for any scholar of that time whether at a seminary or in any other field.
A little background reading from Wikipedia makes this comment about the time of one of his early posts as pastor. In other words he clearly studied Greek early on, then during his first tenure as pastor also took up Hebrew.
He perfected his Greek and he took up the study of Hebrew
Digging a little further, it seems clear that his Hebrew must have been more than a smattering. At one point in his education he was required to translate texts from Hebrew to Latin and Greek and make commentary on it as part of devotionals five days a week. We also find he had at various times at least two qualified tutors in Hebrew, one of which was the author of a Hebrew grammar book of the time. (Source: Hebrew Bible, Old Testament: From the Renaissance to the Enlightenment by Magne Saebo and The Swiss Reformation by Bruce Gordon.)
There seem to be plenty of sources that talk about the education he had and the abilities that those required. Try searching for things like zwingli hebrew on Google Books for further study.