Initially scheduled to be held after midnight, the vote will be held Friday from 1230 GMT onwards because some 230 lawmakers wanted to speak on the issue, the parliament speaker said.
Outside parliament, where hundreds demonstrated against the agreement, riot police fired tear gas to repulse hooded youths who had earlier thrown rocks, France24 reports.
"Tomorrow is a crucial vote... now is the time to break free of the vicious sycle of nationalism and look at... future cooperation," Prime Minister Alexis Tsipras told the chamber.
Macedonia's parliament ten days ago backed a constitutional revision to change the country's name to the Republic of North Macedonia. But for the deal to go through, the change must also be approved by Greek MPs.
Earlier on Thursday, Communist party activists draped giant banners outside the Acropolis, reading: "No to the Tsipras-Zaev agreement."
That was a reference to the landmark compromise agreed in June between Tsipras and his Macedonian counterpart Zoran Zaev.
On Sunday, clashes between police and masked protesters left around 40 people injured as tens of thousands demonstrated in Athens against the name change.
According to the government, "the incidents were provoked by extremists, members of (neo-Nazi party) Golden Dawn, who attempted to enter parliament".
A wide range of Greek political parties, from Golden Dawn to the Socialists, oppose the accord to rename Macedonia.
But it could nonetheless be approved by the required 151 lawmakers in the 300-seat parliament.
The accord aims to start unravelling one of the world's longest diplomatic disputes. The disagreement began nearly three decades ago with Macedonia's declaration of independence but its roots date back centuries.
At least 133 people were detained by the Greek police for the riots that happened on Thursday evening at the Greek parliament during a mass rally against the Athens agreement with Skopje to rename Macedonia, Naftemporiki newspaper wrote on Friday with reference to law enforcement agencies.
According to the newspaper, the Greek police detained 133 people in the area of the central metropolitan Syntagma square, 10 of whom were subsequently arrested for participating in clashes.
The organizers of the protest announced that it would be necessary to continue the struggle and to come to a new meeting on Friday at 11:00 to the parliament. As expected, on Friday afternoon in the parliament will pass a vote on an agreement with Skopje, TASS reports.