Police in the northeastern city of Maiduguri also arrested seven suspected members of the sect who were accused of trying to plant a bomb on a busy street during governorship polls on Tuesday, the state police commissioner said.
"We have seven suspected Boko Haram members in custody, arrested yesterday with a bomb device which they were trying to plant on a busy street in the city," said Michael Zuokumor, referring to the sect.
"They are between 18 and 25 years of age. Another suspected member of Boko Haram opened fire at a polling station in Jajere neighbourhood, killing one voter and injuring four others. He managed to escape in the confusion that followed the attack."
Police in Borno state, where Maiduguri is the capital, also arrested more than 20 other suspects over election fraud allegations, including those accused of attempting to snatch ballot papers.
Maiduguri has long been hit by violence and bomb blasts blamed on the Islamist sect, which launched an uprising in 2009. Three explosions went off Tuesday morning in the city, but no casualties were reported.
Bomb blasts there killed at least three people and wounded 15 on Sunday and Monday.
Most of Nigeria's 36 states voted in state governor polls Tuesday marred by bombs and ballot-box thefts as the country stumbled to the finish line of a landmark election season that set off deadly riots last week.