It invests Norway's revenues from oil and gas production for future generations in stocks, bonds and real estate overseas.
The bank said its analyses of the oil price risk in the government's wealth are based on the government's future oil and gas revenues, the government's direct holdings in Norwegian multinational oil and gas company Statoil and the GPFG.
"It clearly stands out, perhaps not surprisingly, but not obviously, that indeed there is a substantial difference.in return between the oil and gas sector and the broad stock market in periods when the oil price changes substantially", Matsen said.
"Nothing is imminent and even if the advice is fully implemented we believe this will have limited impact on the oil and gas producers, as the holdings of Norges Bank are relatively small and no doubt will be disposed of over an extended time frame", she added.
The Oslo-based fund, which began investing in 1996, has 6% of its money invested in oil and gas stocks.
In September, the fund value reached $1 trillion for the first time after being boosted as the world's major currencies strengthened against the US dollar, combined with strong equity markets.
The fund also held 1.7 percent of Italy's Eni, 1.6 percent of France's Total and 0.9 percent of Sweden's Lundin Petroleum, among others.
Greenpeace Norway welcomed the central bank's intervention, but said Norway must now also cease exploring for oil in the Arctic. At the end of the third quarter, Royal Dutch Shell was the fund's third-biggest equity investment at more than $5bn.
The aim of the proposal is to make Norway's wealth less vulnerable to a permanent drop in oil prices, especially at a time when the fund is increasing the proportion of its portfolio it invests in equities to 70 percent from 60 percent previously.
The Government Pension Fund of Norway, which recently surpassed one trillion dollars in value, is the world's largest sovereign wealth fund.
While Norway has built much of its sovereign wealth through oil and gas development in the past-six percent of the fund is invested in fossil fuels-it's now home to a fast-growing solar power sector, with solar installations rising by 366 percent from 2015 to 2016.
Finance Minister Siv Jensen said in a statement that the concern raised by the central bank was "extensive and has many facets".
At the earliest, the ministry's first opportunity could come in the spring, with a vote in parliament in June.