The clashes occurred in the evening at the Kastanies crossing after riot police came to reinforce security there. No further details were immediately available as officers were keeping media away from the border, citing safety reasons.
Despite a deal reached with the European Union (EU) in 2016, Turkey announced Thursday it would no longer bar the hundreds of thousands of asylum seekers in the country from crossing the border to Europe, a destination they usually prefer.
Ankara said the funds promised by the EU to help it deal with the refugees mainly from Syria and already present on its territory, were slow to arrive. The Turkish government had threatened several times in the past to open its gates if it did not receive more assistance from the bloc.
The announcement that it had stopped containing migrants within the country triggered a rush to the border with Greece, with about 13,000 people reaching it. On Saturday, the Greek government reiterated its promise to keep migrants out.
"The government will do whatever it takes to protect its borders," government spokesman Stelios Petsas told reporters, adding that in the past 24 hours Greek authorities had rebuffed attempts by 4,000 people to cross.
On the other hand, at least 600 people arrived Sunday morning by the sea on the Greek islands of Lesbos, Chios, and Samos close to the Turkish coast, police said.
Turkey currently hosts some 3.7 million Syrian refugees, the largest refugee population in the world.