Police detained a 31-year-old Ukrainian man in connection with the attack.
The stabbing spree on Benedyktyńska Street in Jarosław, in Poland's southeastern Podkarpackie region, left five people injured on Thursday morning, local media reported.
One of the victims, a priest, later died.
Police received a report of the rampage at around 9:30 a.m. Officers arriving at the scene found four men and a woman with knife wounds.
All five were taken to hospital, with three of the men suffering serious injuries, regional police said.
Police detained a 31-year-old Ukrainian citizen at the scene and secured a knife.
According to a nun interviewed by the media, the man entered the abbey through an open gate after a group of young people had left and then attacked people at random.
The motive for the attack had not been established.
Police and prosecutors were investigating the circumstances of the incident.
Local authorities informed schools, public offices and parishes about the incident and advised them to pay particular attention to people entering their buildings.
A crisis management meeting was convened at Jarosław Town Hall following the attack, with the participation of regional governor Teresa Kubas-Hul.
Further details were expected as investigators continued their work.