The UN Children's Rights Committee for the European Union ordered the hatches closed, charging that they violate a child's "right to know and be cared for by his or her parents".
Fr Marian Subocz, director of the Church's Caritas charity, said: "The right to know your identity cannot be more important than the right to life."
He said Caritas had set up 50 "windows of life", operated by nuns, in Poland's Catholic dioceses, which had rescued 44 babies in the past five years.