The attack happened at a Benedictine Sisters monastery on the grounds of the abbey in Jaroslaw, local media earlier reported.
The suspected perpetrator was arrested.
"We know that the act was committed by a 31-year-old Ukrainian national who had entered Poland from Germany earlier today," said Bozena Harasz-Woloszyn from the District Prosecutor's Office in Przemysl.
Harasz-Woloszyn said the attacker used a knife he took from a kitchen on the premises to attack four men and one woman, including one priest who was in a confessional.
"Three of the victims are clergy members and two are laypeople; one person has died," she said.
"Two people are in a critical, life-threatening condition."
The motives behind the attack were not immediately clear.
Police said they were on the scene investigating the incident.
"We are aware that Father Stanislaw has passed away and Father Marek is in serious condition; there are other casualties but we do not have further details," Sister Barbara Dendor told state broadcaster TVP Info.
"When I arrived, there was total panic," she said.
The mayor of Jaroslaw, Marcin Nazarewicz, told a press conference that a period of mourning was being declared until the end of the week.
with DPA
