Bayelsa is the home state of former president Goodluck Jonathan, where incumbent governor Seriake Dickson is running against former governor Timipre Sylva for another four-year term in office.
The woman was shot dead in Oporoma, a town at least 100 kilometres (60 miles) west of Port Harcourt, Nigeria's oil hub which is the capital of neighbouring Rivers state, in one of a series of shooting attacks.
Speaking to AFP, the governor's spokesman Daniel Iwariso-Markson said a woman had been killed in Oporoma, indicating there had also been shooting attacks in Ekeremor, Nembe town and Brass.
Dickson said the attacks targeted his supporters.
"There was a premeditated attack on my supporters in Brass, Ekeremor and Southern Ijaw (municipalities) which left one dead," he told reporters in his hometown, Sagbama.
Some 14,000 police officers have been deployed for the election, but the police had no comment on the violence.
The governor said voter card readers had malfunctioned in several parts of the state, which is home to 1.7 million people.
Jonathan today also complained about the card readers.
Dickson, a 49-year-old lawyer representing Jonathan's Peoples Democratic Party (PDP), is seeking another four-year term in office, while Sylva, 51, is hoping for a comeback in what would be a major victory for President Muhammadu Buhari's All Progressives Congress (APC) in a traditional PDP heartland.
In March, thugs believed to be sympathetic to Dickson invaded a court in the state capital Yenagoa, injuring workers as the court was about to deliver a crucial ruling.
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