Police said they had arrested 60 people accused of trying to breach a razor-wire fence on the border with Serbia.
The state of emergency gives police extra powers and would allow troop deployments if parliament approves.
The EU is facing a huge influx of migrants, many fleeing conflict and poverty in countries including Syria.
Meanwhile, Germany and Austria are calling for a special meeting of EU leaders next week to discuss the crisis.
German Chancellor Angela Merkel told a news conference that "this problem can only be solved together. It is a responsibility for the entire European Union".
The EU's border agency said more than 500,000 migrants had arrived at the EU's borders this year, compared with 280,000 in 2014. The vast majority have come by boat across the Mediterranean.
A boat following the most popular recent route, between Turkey and Greece, sank on Tuesday leaving 22 people dead, Turkish media reported.
Starting on Tuesday, the EU has agreed to relocate 40,000 migrants from Greece and Italy to other EU states. But it has yet to agree on mandatory quotas for a further 120,000 asylum seekers.
After the new Hungarian laws came into effect at midnight (22:00 GMT Monday), police sealed a railway crossing point that had been used by tens of thousands of migrants.
Around midday there were tense scenes as hundreds streamed towards the fence, some searching for a way through and others starting a sit-down strike, throwing down food and water in protest at not being granted passage.