Near the official crossing at Pazarkule, one migrant was shot in the leg as a group of refugees tried to cut their way through the fencing, an AFP photographer said.
The group then threw stones at the Greek police, who responded with tear gas grenades.
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Several Turkish ambulances were seen arriving at the scene.
In a video provided to media by the Greek government, a Turkish police officer appeared to fire a tear gas grenade towards Greek border police.
Large numbers of migrants approached the barbed wire fences early on Wednesday, according to AFP.
Multiple shots and shouts were heard, while smoke appeared to emanate from a large fire.
Cordons of riot police carrying shields lined the Greek side of the border, where the town is called Kastanies.
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