Half the state-owned buildings, which date back to the 18th and 19th centuries, will be turned into homes or small hotels, and the rest will be leased as shops, said Maria Michailidou, head of the antiquities body for the broader Dodecanese island group that covers Rhodes.
"Most of them are in poor condition," Michailidou told AFP.
"Whoever leases them will have the responsibility of restoring them," she said.
The largest island of the Dodecanese, Rhodes was occupied by the Knights of St John of Jerusalem from 1309 to 1523, before they were ousted by the Ottoman Turks and relocated to Malta.
One of Greece's best-maintained medieval monuments and a leading tourist draw, the Old Town mixes Gothic architecture with mosques, public baths and other Ottoman period buildings.
Although the 14 buildings to be leased are not listed monuments, they are still covered by urban planning restrictions, Michailidou said.
A culture ministry statement said the lease period would be 12 years for accommodation use, and six for business use with a possible six-year renewal period. Auction details are expected to be released in a month.
No estimate was given on the total revenues the ministry hopes to raise from the lease.