Nigerian banks have shortened opening times, flights have been cancelled and phone companies may restrict services.
The party of President-elect Muhammadu Buhari has accused the outgoing government of “sabotage” for failing to deal with the crisis.
The wholesale fuel sellers have been withholding petrol as they say they are owed $1bn (£625m) by the government.
The Guarantee Trust Bank says its branches will close at 12:00 GMT as it struggles to get fuel for its generators.
The shortening of its opening times is the latest sign of the impact of the fuel shortage.
Most Nigerian businesses and homes rely on diesel-powered generators because of the poor electricity infrastructure.
The shortage means that Africa’s biggest economy is slowly grinding to halt, says the BBC’s Will Ross in Lagos.
Three of the country’s mobile phone companies, MTN, Airtel and Etisalat, have warned that the fuel scarcity could effect their services as they were finding it difficult to supply diesel to the base stations.
Traffic on the roads is also reducing as many fuel stations have stopped selling petrol and there are long queues at places where they are selling petrol, our correspondent says.
Many domestic flights have been cancelled and some international flights are having to land in neighbouring countries to refuel.
Radio stations are also restricting their broadcasts and some have gone off air altogether.