"Do you want the European Union to be able to prescribe the mandatory settlement of non-Hungarian citizens in Hungary even without the consent of Parliament?" is the referendum question.
Following months of government advertising and publicity, pundits have predicted a solid "no" vote, Xinhua news agency reported.
However, the validity of the referendum is in question, as whether over 50 per cent of all eligible voters would appear and cast valid ballots is unclear.
With a total of 8,272,625 eligible voters in the country, 4,136,313 people will have to cast their ballots, which is doubtful, particularly since the Left-wing opposition has been urging people to shun the referendum.
Poll began at 6 a.m., and will close at 7 p.m.
Hungarian citizens living abroad can only vote at Hungarian embassies or other missions after advance registration. Those ballots will arrive in Hungary later in the week to be counted.
The EU plans to relocate 160,000 refugees from Greece and Italy, the bloc's main entry points for people fleeing war in Syria by September 2017.
Hungary has not accepted a single refugee allocated under the scheme and instead joined Slovakia in filing a legal challenge against it.
In all, nearly 400,000 migrants passed through Hungary last year, en route to Western Europe, primarily to Germany.
While 174,000 people submitted applications for asylum in Hungary, the rejection rate was over 80 per cent. On the other hand, most of the people whose applications were approved have travelled on to other EU countries.
