The break-out took place near the flashpoint town of Roszke where migrants have to wait at a collection point before being taken to a nearby centre for registration.
Shouting “No camp!” they scattered in all directions, some heading for a nearby motorway leading to Budapest which police then closed.
It was the latest in a series of tense confrontations between police and desperate migrants and refugees as the Hungarian authorities struggle to cope with thousands of new arrivals every day.
In the 24 hours to midnight (2200 GMT), 2,770 people were intercepted, police said.
At Roszke, there were 2,529 including 455 children and mostly Syrians, Afghanis and Pakistanis.
On Tuesday, there was a series of similar breakouts in the same area involving several hundred people, with police using pepper spray on one occasion to move a group off a main road.
Hungary’s southern border with Serbia has become a major entry point into the European Union for migrants and refugees fleeing war and misery in the Middle East and Asia.
More than 165,000 migrants have crossed into Hungary so far this year.
Most seek to travel on to Germany via Austria.
Hungary recently completed a razor-wire barrier along its 175-kilometre (110-mile) frontier with Serbia, but it has failed to stop large numbers of people getting through.
It is currently building an additional four-metre (13-foot) fence despite widespread criticism, with France’s foreign minister saying the barrier does “not respect European values”.