The incident happened hundreds of miles from the usual entry point of migrants into the European Union nation.
The boat, carrying about 70 people, ran aground overnight on Sapientza, off the south-western tip of the Peloponnese, the coastguard said.
The vast majority of migrants reach Greece’s eastern Aegean islands, a few miles from the Turkish coast.
Coastguard vessels picked up the migrants yesterday morning, ferrying them to the mainland where they were to be registered. It was not immediately clear where they had set sail from or where they had been going to.
Separately, government figures showed that 261 migrants or refugees arrived on Greek islands in the 24 hours to yesterday morning – a jump compared with recent figures, which had ranged from a few dozen to about 150 per day.
Of those who arrived in the last 24 hours, the vast majority – 139 – reached the eastern Aegean island of Lesbos.
The public order ministry says four Pakistani and two Algerian nationals who had entered Greece illegally were taken back by boat from Lesbos on Thursday. Another eight Syrians were returned on Wednesday on a chartered plane, again from Lesbos.
The new arrivals brought the official count of refugees and migrants stranded in Greece to just over 58,000. Last year, Greece was the main point of entry into the EU for hundreds of thousands seeking better lives. A deal between the EU and Turkey in March, combined with Balkan border closures to migrants, has led to a drop in the number of arrivals.
Those now arriving from Turkey face deportation unless they successfully apply for asylum in Greece. About 11,000 migrants are stranded on a handful of Aegean islands, most housed in overcrowded detention camps.
More than a million refugees and other migrants have reached Greece in smugglers’ boats from Turkey since the beginning of 2015, on their way to Europe’s heartland.
Meanwhile, it was reported that Ankara and Brussels are on a collision course over the migrant deal. Turkey has repeatedly warned it will walk away from the agreement to accept refugees heading to Europe unless the EU agrees to waive visa restrictions.
President Recep Tayyip Erdogan argued Brussels had little choice in the matter, saying: “Our nation is taking care of around three million Syrians. EU countries have taken just 3,000, 5,000 or 10,000 people. European countries don’t know what to do. They were at the point of ignoring human rights.”
Visa-free access to the EU has been delayed due to a dispute over Turkey’s anti-terror laws and a post-coup crackdown.
Germany’s European affairs minister, Michael Roth, said: “Turkey faces a very long and difficult path. The criteria must be fulfilled, and it doesn’t look good at the moment. But I want to make clear that we want and need a European Turkey.”