Cardinal Kazimierz Nycz made the appeal in a pastoral letter released by Catholic media on Wednesday and which is to be read in churches in his diocese on Sunday.
It concerns "the image of Poland and of the Church of Poland," Nycz said, adding he was counting on some "opening up" from the government on the issue.
The ruling conservative Law and Justice party (PiS) opposes the entry of Muslim refugees and migrants on security grounds, and has rejected an EU plan to share out migrants among the member states.
The government's view is shared by a significant portion of Poland's ethnically homogenous population of 38 million people.
But the cardinal said that a system known as "family to family" assistance between Polish and Syrian families has already been operating discreetly for several months.
"We hope that the next step will be an aid programme through humanitarian corridors. It will involve welcoming in Poland a few hundred refugees in need of urgent medical care, of exceptional assistance, necessary to keep them alive", the archbishop's letter said.
"This programme is therefore safe" from a security point of view, he added.
Caritas Poland, the Catholic Church's humanitarian organisation, is ready as well as the Catholic dioceses, according to the archbishop.
Minister of Family and Labour Elzbieta Rafalska responded by saying that "the government can understand such an appeal.
"But if we talk about concrete solutions, we need to know who (the refugees) are and what the scale of assistance should be," she told a private radio station.
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