There have been long queues at some banks as Nigerians have struggled to meet the original deadline of Tuesday.
People now have until 10 February to do the swap.
The redesign of the higher denomination naira notes has been heavily criticised with analysts saying six weeks was not enough time for Africa's most-populous country to phase out the old currency.
It is happening a few weeks before the country goes to the polls in presidential and parliamentary elections.
Local media has been reporting that there are not enough of the new notes in circulation, with people unable to withdraw them from banks.
The move by the the Central Bank of Nigeria (CBN) is seen as a push to encourage Nigerians to embrace digital payments in a society where cash is king.
It hopes the exchange will bring some of the cash currently being hoarded by individuals and companies back into the banking system.
When the bank announced in October that the 1,000 ($2.18, £1.75), 500 and 200 naira notes were to be replaced, it said 80% of the notes in circulation were outside banks.
The CBN believes that with the redesigned currency it will have a better understanding of the money circulating in the economy so it can better manage inflation.
The bank governor said the new deadline of 10 February would allow more people in rural areas, where there are very few bank branches, to exchange the old notes.
He added that Nigerians would then have a further seven days to deposit old notes directly with the CBN.