Knossos Palace in Crete was one of the priceless items put into the fund - a holding company owned by the Greek state - to satisfy Greece's foreign creditors under the last financial bailout in 2015.
The fund also oversees several state utilities, a bailout fund for Greek banks and the privatisation agency.
The government has repeatedly denied the site and monuments could be sold, but that has not prevented protests, including a one-day strike by archaeologists in October which closed the Acropolis, an attraction for millions of Athens visitors every year.
"The cultural assets are exempted," Culture Minister Myrsini Zorba told reporters on Tuesday, announcing a ministerial decree on the matter. "We have 2,330 assets which are protected through a legal act and we can now rest."
One of those assets is Spinalonga, a small island that was a leper colony until 1957 and featured in Victoria Hislop's best-selling book "The Island".
Zorba said a full list of the assets would be published later.