Polling stations in both cities opened on Sunday morning and will be open until 6 p.m. local time (1700 UTC). Up to 1.3 million people could cast their votes in Germany's biggest port city. At midday, turnout in Hamburg was high. Many residents had also cast votes via postal ballot.
Nearly 200,000 people in the northern port city of Kiel are also eligible to vote as the sailing competitions would take place there if the bid proved successful.
Hamburg is one of the cities planning a bid to host the 2024 Olympic and Paralympic Games. The games have not been hosted in Germany since the infamous 1972 Summer Games in Munich that were overshadowed by a massacre that left 11 Israeli athletes, a German police officer and five Palestinian terrorists dead.
A bid to host the Winter Games in Munich in 2022 failed to get off the ground after residents voted "no" in a referendum.
Hamburg's senate estimates the costs of hosting the two events at about 11.2 billion euros ($11.9 billion), with revenues forecast at about 3.8 billion euros.
Critics are concerned about where the funds would come from, as Mayor Olaf Scholz has already said Hamburg could only come up with 1.2 billion euros. The remainder would have to come from the federal government, which, so far, has not made a firm commitment to that effect.
Hamburg lawmaker Walter Scheuerl tweeted: "Storm over Hamburg. This is not for the fainthearted and 'Yes' sayers. Stop the waste of billions on the Olympics today!"
The "no" camp has also raised concerns about security following the recent terror attacks in Paris.
Those in favor of the bid - like Bayern Munich defender Philip Lahm - took to Twitter to point out that "everyone stands to gain from such unique events, vote 'yes'"
The German Olympic Sports Federation needs more than a simple majority to be able to launch a bid. If fewer than 20 percent of all eligible voters in Hamburg and 8 percent in Kiel vote 'yes,' it has to withdraw the bid.
The International Olympic Committee will decide on the host country for the 2024 Olympics next year in Lima, Peru. Budapest, Paris, Rome and Los Angeles are also planning to launch a bid.
Results are expected after 10 p.m. Sunday.
ng/jlw (dpa, AP)