The original Venetian term was arzenale. This can be traced back to the Arabic dār-aṣ-ṣinā‘a (lit. house-of-industry). It might seem surprising that an Arabic word was used, but a look at the word for 'dock' in Italian (darsena) suggests a possible route.

Darsena has a Spanish cognate, dársena, and Spanish also has atarazana, meaning shipyard, both with the same Arabic root. The most likely explanation is that they entered Spanish through the Andalucian dialect and then on to Italian through trade. Catalan uses darsena as well, while French uses darse, so there's a clear line of etymology that you can follow. The Latin equivalent is navale, which further suggests that the term was imported.