Central European countries have reacted angrily after plans to relocate 120,000 migrants across the continent were approved by EU interior ministers.
Under the scheme, migrants will be moved from Italy, Greece and Hungary to other EU countries.
But Romania, the Czech Republic, Slovakia and Hungary voted against accepting mandatory quotas.
Czech President Milos Zeman said: "Only the future will show what a mistake this was."
The BBC's Europe correspondent Chris Morris says it is highly unusual for an issue like this - which involves national sovereignty - to be decided by majority vote rather than a unanimous decision.
The scheme to take in migrants appears on the surface to be voluntary, he says, although countries are likely to be given little choice in the matter.
Under the EU's rules, a country that does not agree with a policy on migration imposed upon it could have the right to appeal to the European Council.
But Luxembourg Foreign Minister Jean Asselborn, who chaired the meeting, said he had "no doubt" opposing countries would implement the measures.
Finland abstained from the vote. Poland, which had originally opposed the proposal, voted for it.
"We felt that it was much better to negotiate, to negotiate all these conditions, which for us are important," Poland's Europe minister, Rafal Trzaskowski, told the BBC.
"We preferred to be an active member of this debate."
The scheme must now be ratified by EU leaders in Brussels on Wednesday.
Under the plan, Hungary will have to take in a share of migrants. Had it not opposed the scheme, it would have been exempt.
Hungary's anti-immigration Prime Minister Viktor Orban could present his own proposals before EU leaders on Wednesday.
The UN refugee agency said the scheme would be insufficient, given the large numbers arriving in Europe.
"A relocation programme alone, at this stage in the crisis, will not be enough to stabilise the situation," , UNHCR spokeswoman Melissa Fleming said.
The number of those needing relocation will probably have to be revised upwards significantly, she said.
The UN says close to 480,000 migrants have arrived in Europe by sea this year, and are now reaching European shores at a rate of nearly 6,000 a day.
After the meeting, German Interior Minister Thomas de Maiziere said: "Today is an important building block, but no more than that."
A statement from the European Commission said foreign ministers would now discuss reforms to the Dublin regulation, which demands that migrants register as refugees in the first EU country in which they arrive.
The UK has opted against taking part in the relocation scheme and has its own plan to resettle migrants directly from Syrian refugee camps.