The poll took place a week after the national elections in the northern Hamburg country on Sunday.
The polling station opens at 8 a.m. GMT (0700) and will be closed at 6 p.m., which will be the only election in Germany this year.
Hamburg is one of three city-states in Germany, with Berlin and Bremen.
The Social Democrats (SPD) who suffered a crushing defeat in the federal election last Sunday and is expected to remain the biggest force in port cities, with Mayor Peter Tschentscher hoping to create another alliance with the Greens.
Nearly 1.3 million residents are eligible to vote in Hamburg, whose voting age is 16.
One third of those eligible to vote may have voted.
More than 420,000 postal voting documents have been released by Friday – much more than during the last Hamburg election five years ago, according to the state election office.
