
The footage was sent by a volunteer on the Greek island of Lesbos, who says the incident happened on Saturday.
The migrants accused Turkish coast guards of attacking them. But the coast guards say they try to stop boats without harming the occupants.
The EU and Turkey are discussing new moves to curb the flow of refugees.
Europe is facing its biggest refugee crisis since World War Two. Last year, more than a million people entered the EU illegally by boat, mainly going from Turkey to Greece.
Most of them were Syrian, fleeing the country's four-year civil war. Another 2.7 million Syrian refugees are currently in Turkey, which is struggling to cope with the influx.
More than 132,000 migrants have arrived by boat into Greece so far this year - a large increase on the same period last year.
The volunteer who handed the latest video to a BBC correspondent in Lesbos said the incident occurred in Turkish waters opposite the island.
The 30-second clip shows people wearing life jackets on a rubber dinghy being hit with poles by men standing on another vessel. The people being hit speak Farsi and Arabic, while the men on the other boat speak Turkish.
The boat of migrants eventually moved away and made it to Lesbos. There is no confirmation of the authenticity of the video, but the Turkish coast guard later said: "We try everything to stop dinghy engines without harming refugees on board."
Our correspondent says he has heard of similar incidents involving other migrants.
BBC/RI