The blaze happened at the Independent National Electoral Commission (INEC) Office in the Qua’an Pan area of Plateau state late on Saturday.
The INEC head of voter education and publicity in Plateau state, Osaretin Imahiyereobo, said of this latest incident: “A drunken security man was said to have caused the fire outbreak.”
Imahiyereobo said the office was “completely burnt with all its contents”, including ballot boxes and uncollected voter ID cards.
A similar fire broke out last weekend in the southeastern state of Abia.
Nigeria goes to the polls next Saturday to elect a new president and parliament. State governorship and local assembly elections follow on March 2.
President Muhammadu Buhari, of the All Progressives Congress (APC), is seeking re-election. His main challenger is Atiku Abubakar, of the Peoples Democratic Party (PDP).
The race is expected to be close but both parties have been accused of trying to rig the vote, particularly by buying voter cards.
INEC on Friday extended the deadline for collection of the cards until Monday, after complaints they were not ready.
Plateau state, which lies between the mainly Muslim north and largely Christian south, has been the centre of renewed violence in the long-running conflict for resources between nomadic herders and farmers.
Buhari has been criticised for his response to the violence because he is also a Hausa-speaking ethnic Fulani Muslim like the herders.
He has repeatedly denied the charge but it has raised the chances of him losing states in the north-central zone affected by the conflict, which swung from the PDP to APC in 2015.
Buhari was elected on a pledge to tackle endemic corruption but his high-profile campaign has been seen as one-sided in that it has mainly targeted political opponents.
He wrote in an article published on Sunday that Nigeria’s main anti-corruption agency had “raised concerns over laundered money being funnelled into vote-buying”.
“This is the problem of corruption writ large,” he wrote on the Pulse Nigeria website in a lengthy defence of his campaign against graft.
“It illustrates how it lurks in all and every crevice of public life, manipulating due process in pursuit of self-preservation and perpetuation; protecting personal political and economic interests at the expense of the common good.”