Faxe Municipality is a kommune in Denmark in the Region Sjælland on the island of Zealand. The municipality covers an area of 406 km and ha…Faxe Municipality is a kommune in Denmark in the Region Sjælland on the island of Zealand. The municipality covers an area of 406 km and has a population of 37,753. Its mayor as of January 2018 is Ole Vive. He is a member of the agrarian liberal Venstre political party.