Macedonian police have fired tear gas at a crowd of migrants who destroyed a barbed-wire fence on the Greek border using a makeshift battering ram.
TV footage showed migrants pushing against the fence at Idomeni in Greece, ripping away barbed wire.
A section of fence was smashed open with a metal signpost. It is unclear if any migrants crossed the border.
About 7,000 people are stuck on the Greek side of the border, as Macedonia is letting very few in.
Many have been camping in squalid conditions for a week or more, with little food or medical help. Most of those trying to reach northern Europe are Syrian and Iraqi refugees.
The chaos on Monday erupted as hundreds of people pushed their way past Greek police, shouting "Open the border!", to reach the gate used to let trains through at the border crossing. Some threw stones at Macedonian riot police.
Macedonia and some other Balkan countries have erected fences in an attempt to reduce the influx of migrants, after more than a million reached Germany last year.
Greece is angry with Austria further north for having imposed a cap on migrant numbers. The crisis has left Greece shouldering much of the burden of housing migrants arriving in the EU from Turkey.
Many are refugees fleeing war in the Middle East, while others are escaping human rights abuses in Afghanistan, Eritrea and other conflict zones.
In other developments on Monday:
- French bulldozers began demolishing shacks in the "Jungle" migrant camp in the northern port city of Calais, though some communal facilities were left standing
- The Dutch government said there were 30 war crimes suspects among migrants who claimed asylum in the Netherlands last year - 10 from Syria and the other 20 mostly from Eritrea, Nigeria, Sudan and Georgia
On Sunday, German Chancellor Angela Merkel urged Europe to help Greece in the current migrant crisis.
In a TV interview she said: "Do you seriously believe that all the euro states that last year fought all the way to keep Greece in the eurozone, and we were the strictest, can one year later allow Greece to, in a way, plunge into chaos?"
She defended her decision last year to allow migrants in without a cap on numbers, saying she had no "Plan B".
She has insisted that Germany can cope with the influx - and has a humanitarian duty to look after war refugees.
But her stance has been strongly criticised by some EU neighbours and some politicians in her ruling conservative CDU-CSU bloc.
Analysis: Damian Grammaticas, BBC News, Brussels
Europe has come up with a whole slew of policies to deal with this refugee crisis. Some of them were being debated in Brussels today: creating a single coastguard and border force with the power to intervene directly in member states; systematic checks on everyone crossing Europe's external borders; deporting more failed asylum seekers.
But part of the EU's problem is that events on the ground are moving faster than the policies are being implemented.
Individual countries like Sweden, Denmark and Belgium have broken ranks and imposed their own border checks. Others have failed to take in refugees. Angela Merkel pointed her finger squarely at Austria, saying its decision to accept just 80 refugees a day had led to today's problems in Greece.
Europe's leaders have a chance to restore some unity at another crisis summit in a week's time. But it may be events on Greece's borders that dictate what happens.
Greece, under intense pressure from anxious EU partners, has erected extra reception centres on the Greek islands near Turkey, where thousands of migrants have been arriving daily.
The number of people who arrived into Greece in only two months this year is already more than three times higher than all the arrivals in 2014.
Austria and Hungary have adopted a tougher stance than Germany. Hungary has fenced off its southern border and refuses to take in any non-EU migrants.
"Tragically, there seems to be more willingness among European countries to co-ordinate blocking borders than to provide refugees and asylum seekers with protection and basic services,'' Giorgos Kosmopoulos, Amnesty International's director in Greece, told AP.