He said Greece was only interested in any items illegally exported and would be satisfied if Christie's proved their legal origin.
"You are solely responsible of ensuring that all potential buyers know ... of our clients' strong reservations," said the letter, released by the ministry.
"If I were a buyer, I'd think about it," the culture minister said.
The collection includes about 850 paintings, due to go under the auctioneer's hammer on Wednesday and Thursday.
Greece has asked Christie's to shelve the auction until it explains how it obtained the collection of King George I, who ruled Greece from 1863 until 1913.
Some items are forecast to fetch up to $496,000.
Christie's said all the works were legally obtained and it saw no reason to cancel the sale, which has attracted extensive international interest.
The collection comes from the summer palace of Tatoi in Greece and was released to ex-king Constantine in 1991.
According to the ex-king's website, the items were the personal property of members of the Greek royal family and are no longer in his possession.
Constantine fled the country after briefly co-operating with the 1967-1974 military junta and lived in exile for decades.
In 1991, the then ruling conservatives allowed him to export the contents of Tatoi.