Rav Avraham Shapiro, a chief rabbi of Israel, wrote the following:
"There is no conflict between democracy and halacha. Throughout the long years of Diaspora the Jewish People maintained their existence everywhere by means of independently elected community institutions. They lived in a completely democratic manner, as we learn from the writings of the Poskim who discussed matters pertaining to the community's mode of life."
Once Moshiach arrives, some probably believe that he will create a monarchy with most powers of government vested in him. I'm not sure if this is required under Jewish law, however; it's possible that democracy could continue even during the Messianic age.