"The first Jews were allowed to settle in Venice
only in 1385, when the city was involved in a war against
neighbouring Chioggia and needed loans from the Jewish
money-lenders.

But racism persisted, and in 1516 Venice's ruling council confined
all the Jews in a smallen getti, or foundries."

But that still doesn't give any clue as to how the word spread so far.

P.S. I found a site about Jewish history in Venice. Persecution elsewhere in Europe led many Jews
to come to Venice. It seems possible that when persecution in Europe seemed less active, Jews
from from Venice moved into Europe and took the word "ghetto" with them.