The move shows the determination in Brussels to enforce the controversial scheme launched at the height of the migrant crisis in 2015 to share 160,000 refugees around the bloc and ease the burden on Greece and Italy.
"The European Commission has today decided to refer the Czech Republic, Hungary and Poland to the Court of Justice of the EU for non-compliance with their legal obligations on relocation," the commission said in a statement.
Brussels launched so-called infringement proceedings against the three countries in June for failing to take in any refugees under the quota system, and warned them last month of further action.
They face heavy fines for failing to comply with any eventual ruling by the Luxembourg-based European Court of Justice.
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The ongoing row over the quota scheme has held up efforts to reform the bloc's asylum system, which leaders are supposed to be discussing at an EU summit in Brussels on December 14- 15.
The row also underscores a growing rift between western European states and newer, former Soviet-bloc states in the European Union over a series of issues from migration to democratic standards.
Budapest faced a triple legal whammy from Brussels on Thursday, with the European Commission also taking Hungary to the ECJ over a crackdown on education and foreign-backed civil society groups that critics say targets US billionaire George Soros.
It said in a statement that it was suing Hungary as the education law "disproportionally restricts EU and non-EU universities in their operations and needs to be brought back in line with EU law."
Hungary has introduced an education law that could shut the Soros-founded Central University in Budapest, which has long been seen as a hostile bastion of liberalism by Orban's right-wing government.
In June, Hungary approved a law aimed at forcing civil society groups receiving more than 24,000 euros ($26,000) annually in overseas funding to register as a "foreign- supported organisation", or face closure.
Poland's rightwing government is also in the EU's legal crosshairs.
Last month the ECJ warned Warsaw to stop logging in one of Europe's last primeval forests "immediately" or face fines of up to 100,000 euros a day.
The European Parliament also voted to start an EU sanctions procedure over Warsaw's controversial judicial reforms that could eventually suspend Polish voting rights in the bloc.