One bank has emailed customers to this effect, stressing it is a “temporary measure”.
Access to foreign online retailers will also be affected when the ban takes effect on 1 January 2016.
It is part of the government’s effort to try to stem the flow of foreign exchange out of the country.
The unofficial value of the Nigerian currency, the naira, has plunged because of the fall in the oil price – its main export.
Africa’s largest economy has spent billions of dollars propping up the currency since it fixed the exchange rate in February and tightened trading rules to curb speculation.
It is not clear how many people will be affected by the latest measure but the BBC’s Bashir Sa’ad Abdullahi in the capital, Abuja, says wealthy Nigerians travel abroad regularly and use their local cards for shopping and other transactions.
Some top-end shops in London have signs in Hausa to cater for the large number of Nigerian customers.
One of the banks, Standard Chartered, has emailed its customers notifying them of the ban.
In June, the central bank banned businesses from accessing hard currency to import about 40 items.
The list included Indian incense, plastic and rubber products, soap and even private jets.
The amount that Nigerians could spend on credit cards abroad has already been reduced by the banks.