Jinan Boushehri, 32, said on Sunday: "I felt I was able to add something to municipal work, and I have the right credentials."
The seat became vacant when Abdullah al-Mhailbi, the council speaker, was appointed to the new cabinet on Thursday. He was given the portfolio of municipal, agricultural and environmental affairs.
No date has been set for the by-election.
Soon after the legislature voted last May to allow women to cast ballots and run for public office, the government appointed two women to the partly elected Municipal Council, which is responsible for zoning and planning.
Ten of its members are elected and six appointed by the government.
Boushehri heads the food-testing section in the municipality, and has a master's degree in chemical engineering.
Last year, the government also appointed the country's first female cabinet member, Massouma al-Mubarak.
She kept her position as minister of planning and administrative development in the new cabinet.
The country's next parliamentary elections are due to take place next year.
Women have been automatically registered as voters, adding 194,614 to voter lists that already had 139,179 men.