The proposal, submitted by the government, allows people to vote without any ID as long as they are accompanied by two people who vouch for their identity.
The opposition had challenged the proposal in court but the Constitutional Court on Saturday "rejected the opposition's request," the number two of the National Independent Electoral Commission (CENI), Kadri Oumarou Sanda, told AFP.
"We were right in authorising it," he said. The poll body had okayed the proposal submitted by Prime Minister Brigi Rafini earlier in the week.
"The prime minister's move is an ill-disguised attempt by the government to disrupt the elections," said Tahirou Kalilou from the opposition COPA 2016 grouping.
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Amadou Boubacar Cisse, who is contesting for the presidency, said it was an "abuse of power and violation of electoral law."
The move affects about 1.5 million of the 7.5 million registered voters who were found not to have any identity papers.
"This can pave the way for fraud," said Moussa Tchangari, a leading civil society figure.
Issoufou hopes for a "knockout" first-round majority victory but that would be a first in the country's short history of multi-party democracy, beginning in 1990.
Results are due within five days of the vote.