The refugees had squatted on rail lines in the Idomeni area on Monday after attempting to push through the border to Macedonia, angry at delays and additional restrictions in crossing. They were expected to be taken to relocation camps inside Greece.
Greek police and empty buses had entered the area before dawn, a witness said. In one area seen from the Macedonian side of the border, about 600 people had been surrounded by Greek police, the witness said.
There were an estimated 1,200 people at Idomeni, in their vast majority Afghans or individuals without proper travel documents, Reuters reported.
A crush developed there on Monday after Macedonian authorities demanded additional travel documentation, including passports, for people crossing into their territory.
Some countries used by refugees as a corridor into northern Europe are imposing restrictions on passage, prompting those further down the chain to impose similar restrictions for fear of a bottleneck in their own country.
But there are concerns at what may happen in Greece, where an influx continues unabated to its islands daily from Turkey. On Tuesday morning, a further 1,250 migrants arrived in Athens by ferry from three Greek islands.
"It's a difficult management exercise. I don't know if the planning is adequate. The flows are increasing, more ships are coming," Piraeus mayor Yannis Moralis told Mega TV during a visit at the port's station where refugees had gathered.
He said the port's terminals were full, mostly with women and children. "It's a difficult situation, not only for Piraeus but for the country as well."
Some of the migrants had bus tickets to Idomeni, but it was unclear if they would be permitted to travel north from Athens.