The Independent National Electoral Commission said on Tuesday evening that the fire -- the third at INEC offices in the last 12 days -- broke out in Anambra state.
"There was no fatality or injury reported. Initial assessment, however, confirms that a total of 4,965 of the Smart Card Readers were destroyed in the inferno," it added.
The machines would have been used to read biometric identity cards containing personal details of voters at Saturday's presidential and parliamentary elections.
The head of INEC's information and voter education committee, Festus Okoye, said the loss of the machines was "a setback" but spare readers were being deployed from elsewhere.
"With the steps so far taken, the commission remains confident that the election in the state will proceed as scheduled," he added.
Previous fires have occurred in Abia state, also in the southeast, and the central state of Plateau, destroying ballot boxes and other election materials. INEC blamed "a drunken security man" for the Plateau fire. The Anambra blaze has been referred to the police and fire service for investigation.
Concerns have been raised that this weekend's poll, plus governorship and state assembly elections on March 2, could be hit by vote-buying. INEC chairman Mahmood Yakubu warned last month there had been attempts to buy permanent voter cards.
At the governorship election in the southwest state of Ekiti last year, the two main parties were accused of offering voters 3,000-5,000 naira ($8-13, 7-12 euros) for their cards.
A deadline for collection of cards was extended last week, after complaints of slow distribution and delays.
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