TV footage showed migrants pushing against the fence at Idomeni, ripping away barbed wire, as Macedonian police let off tear gas to force them away.
A section of fence was smashed open with the battering ram. It is not clear how many migrants got through.
Many of those trying to reach northern Europe are Syrian and Iraqi refugees.
About 6,500 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.
The chaos on Monday erupted at a gate festooned with barbed wire, keeping migrants away from a railway line.
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 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.
Map of Idomeni on Macedonia-Greece border
Migrants fleeing tear gas on border, 29 Feb 16Image copyrightAP
Clouds of tear gas fired by Macedonian police forced migrants to flee the scene
Idomeni border clash, 29 Feb 16Image copyrightAP
Macedonian police confronted hundreds of angry migrants at the fence
In other developments:
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
Merkel defends welcome
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”.
Map locatorImage copyrightAFP
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.
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.
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.