The Blue Star 1 took 35 of the survivors aboard and carried them to safety on Lesbos, where they joined the rest of the group, who were picked up by the port police on speedboats.
Passengers on the Blue Star 1 raised the alarm after seeing the migrants' overloaded boat was on the verge of sinking.
Lesbos is one of several Greek islands struggling to cope with an influx of thousands of migrants, many of them Syrian refugees, setting sail from the nearby Turkish coast.
Most of those onboard the ferry today were Afghans, an AFP journalist said, in contrast to previous crossings which have mostly transported Syrians.
There have been clashes on Lesbos in recent days between police and migrants, and between migrants of different nationalities, over delays in the registration process that have held up their journeys on to other countries in Europe.
More than 230,000 people have landed on Greek shores this year, with the numbers soaring in recent weeks as people seek to take advantage of the calm summer weather.
Port police said the Greek coastguard had rescued a total of 2,600 refugees and migrants between Friday and morning, a count that does not include those who managed to make it to the islands on their own.
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