Thirty-seven people were rescued from the ship, the ministry said in a statement on Friday, which sank some 259 km (161 miles) southwest of the Turkish resort of Kas on Thursday evening.
Turkish Navy ships and an aircraft were involved in the search and rescue operation, the statement added.
There was no immediate information on the nationalities of those involved.
Migrants and refugees often use Turkey as a gateway to join the European Union, mainly via Greece.
Many depend on smugglers and risk their lives through perilous journeys in overcrowded boats.
In 2016, Turkey signed an agreement with the EU aimed at limiting the arrivals of migrants and refugees from the country to Europe in exchange for certain incentives, including financial assistance.
Turkey currently hosts some 3.7 million Syrian refugees.
President Recep Tayyip Erdogan has long called for more EU help dealing with refugees and has already threatened to open the Turkish border if the bloc does not provide additional funds.
In June, EU leaders gave the green light to plans to give Turkey an additional three billion euros ($ 3.6 billion) over the next few years to provide further assistance to Syrian refugees on its territory and help the country strengthen border controls.
The plan for the new funding is part of a series of incentives the bloc is using to try to keep Erdogan on the side, with Brussels also offering to modernize a customs union with Turkey and start high-level talks on issues ranging from health to safety.
But Turkey called the reduction of cooperation on migration to a financial dimension a “big illusion” while urging more cooperation with the bloc to tackle the problem.
Ankara has repeatedly stated that it wants the 2016 agreement to be revised in a way that “meets the needs of the day and common interests”.
Turkey now fears a new wave of migrants and refugees from Afghanistan after the United States withdrew its troops from the country after years of fighting against the Taliban armed group, which recently regained territory.
Erdogan said this week that Ankara was in talks with Afghan authorities over the issue of possible arrivals of migrants and refugees.