A woman was hit on the head by a rock, and a man was being treated for breathing trouble, health officials said.
Some 500 demonstrators, waving Greek flags, had tried to approach the signature ceremony on the banks of Lake Prespa on the other side of the mountain from where the protest took place.
But they were surrounded by police near the small village of Pisoderi, some 25 kilometres (16 miles) away from the ceremony.
One detachment of riot police blocked the rural road leading to the lake, while others on mountain slopes threw stun grenades and tear gas at the crowd.
The authorities said some 5,000 people had earlier taken part in the protest against the agreement.
"We are fighting for the land of our fathers. We are not backing down," a protester said.
While the demonstration took place, the foreign ministers of Greece and Macedonia signed a preliminary accord to rename the country the Republic of North Macedonia, a move hailed by the European Union, the United Nations and NATO.
Since 1991, Athens has objected to its neighbour being called Macedonia because it has its own northern province of the same name, which in ancient times was the cradle of Alexander the Great's empire -- a source of intense pride for modern-day Greeks.
At the fishing village of Psarades, where the deal was signed, priests tolled the local church bell in a sign of mourning, an AFP reporter said.
On Saturday, police guarding parliament had also clashed with protesters as Tsipras defeated a vote of censure against his government.
The government has blamed the incidents on far-right hardliners.
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