In a letter to the government, the bank said that if the world's largest sovereign wealth fund — commonly referred to as the “oil fund” — were to divest its oil and gas shares, Norway would be less vulnerable to a lasting decline in oil prices.
The Scandinavian country is western Europe's biggest oil and gas producer.
The sector accounts for 14 percent of Norway's gross domestic product. Any fall in crude prices, as has been the case since the summer of 2014, affects the state's revenues and the fund's investments, upon which the state is increasingly dependent to balance its budget.
“This advice is based exclusively on financial arguments and analyses of the government's total oil and gas exposure,” the bank's deputy governor Egil Matsen said in a statement.
It “does not reflect any particular view of future movements in oil and gas prices or the profitability or sustainability of the oil and gas sector,” he added.
The bank recommended the removal of oil stocks from the fund's benchmark index, which would still give it a little leeway to invest modestly in the sector.
The finance ministry said it would present its conclusions in the autumn of 2018.
“The problem raised by the central bank is extensive and has many facets,” Finance Minister Siv Jensen said in a statement.
“The government is responsible for the Norwegian economy in its entirety and has to adopt a broad and comprehensive approach to this question,” she added.
The sovereign wealth fund, fuelled by the state's oil revenues which have dropped sharply in recent years, is currently worth around 8.24 trillion kroner (854 billion euros), invested primarily in shares (65.9 percent) as well as bonds and real estate.
The oil and gas sector accounts for 5.5 percent of its equity investments.
The Norwegian fund has already divested from coal for both environmental and financial reasons.
The future of Norway's oil sector is at the heart of a lawsuit brought this week against the state by Greenpeace and two other environmental groups, protesting against the awarding of exploration licences in the Arctic.