Voting began at 8am (0500 GMT) on Thursday in the 10 electoral districts and were to continue until 8pm (1700 GMT).
Turnout was low in the morning, with only a few dozen citizens casting their vote in each constituency. Thursday is a weekend holiday in this Muslim state.
The elections were being held under tight security, and the Interior Ministry mobilised part of its forces to maintain law and order.
Results, with the votes counted manually, were not expected before midnight local time.
Voters are to elect 10 members of the 16-seat civic body. The remaining six members are appointed by the ruler of the country on government recommendation.
Fifty-four candidates are contesting the polls, many of them backed by political groups and tribes.
There are 130,000 eligible voters in Kuwait, which has a native population of 956,000.
This will be the last election in which women will not vote after parliament on 16 May voted to grant women full political rights.
Enfranchised Kuwaiti women will make their election debut in the 2007 legislative elections and will vote in the next municipal polls in 2009.