While perusing adult content, the minister inadvertently downloaded malicious code, which crashed the local network.
According to the English-language Swedish newspaper, The Local, "the Church of Sweden official admitted to spending a lot of time at work viewing adult material," the report said.
"He recently decided to resign," Charlotta Novosel, a legal spokeswoman for the church, told the online publication.
Church authorities have not yet decided whether the minister should be formally disciplined.
"Priests are people too," Archbishop Anders Wejryd told the paper. "But I have no understanding at all for someone sitting and surfing for porn on the parish computers," he added.
Sexual misconduct among Swedish clergy evidently has been reported frequently. Previously, a pastor in Gothenburg was questioned for moistening Post-it notes with his penis.
After an official review, authorities took no further action in that case.