EU Home Affairs Commissioner Ylva Johansson said the scheme was "a window of opportunity for a targeted group," adding that the International Organization for Migration (IOM) would handle the plan with the EU border agency Frontex.
"Refugees will not return, of course, they can't return, but economic migrants that maybe know they will not get a positive asylum decision could be interested in doing that," Johansson told reporters.
She said the scheme could be a fast way to alleviate the pressure on Greek islands' camps, where conditions are "totally unacceptable." It is only open for one month and reserved for migrants who arrived before 1 January.
Hundreds of migrants and refugees have reached Greek islands near Turkey in February, increasing the strain on already struggling centers that receive seven times more people than their capacity permits.
Aid agency Medecins Sans Frontieres (MSF), which is working on the islands, says more than 14,000 of the migrants are children.
"Men, women, and children are living in horrific conditions in these overcrowded centers, in constant fear and with very basic access to services like toilets, showers, electricity," Stephan Oberreit, MSF head of mission in Greece, told the BBC.
"Our teams in the clinic opposite Moria camp receive around 70 children per day, including children suffering from chronic illnesses, for which we are not able to provide proper care."
Johansson said seven EU member states, including Croatia, Ireland, Finland, France, Germany, Luxembourg, and Portugal, agreed to take in at least 1,600 unaccompanied vulnerable children from the camps.
Many of the migrants are Syrians fleeing the civil war, but there are also Afghans, Pakistanis, and West Africans.
Aid agencies consider Syria too dangerous for migrants to be sent back there, but some other countries, such as Pakistan, are considered safe enough.
The latest surge in numbers at the Greek border came after Turkey announced that it would no longer stop migrants from trying to enter Greece. Turkey currently hosts some 3.7 million Syrian refugees, the largest refugee population in the world. The country accuses the EU of not doing enough to help.