Two women are also among eight candidates running for the seat in the Salmiya district, south of the capital.
60% of the 28,000 eligible voters are are women, and are voting in segregated polling booths demanded by Islamist and tribal MPs.
Women were granted equal political rights last year and will vote in full legislative polls in 2007.
Voting was reported to have begun slowly, as Tuesday is a normal working day in the conservative, oil-rich state.
Source: BBC News