The attacks happened in the villages of Birin Bolawa and Birin Fulani in the Nafada district of Gombe state, which has been repeatedly targeted by the Islamists.
An election official, who requested anonymity, said: "We could hear the gunmen shouting, 'Didn't we warn you about staying away from (the) election?'," the election official said, requesting anonymity.
Boko Haram leader Abubakar Shekau said in a video message last month that the militants would disrupt the election, which they see as "un-Islamic".
The threat and a spate of suicide attacks and bombings against "soft" targets in restive northern Nigeria have prompted the authorities to impose tight security across the country.
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The election official said the masked gunmen arrived in Birin Bolawa in a pickup truck at about 8:30 am (0730 GMT), just after accreditation for today's presidential election had begun.
One voter was shot dead and others fled in panic.
"They set fire to all the election materials we abandoned as we escaped," he added.
"As soon as people saw them they began to run away but the gunmen opened fire on the polling station, killing one man," he said.
"They burnt the election materials. We strongly believe they are Boko Haram who have been warning people not to participate in the elections.