The man had allegedly made complaints about Fr Brunissen trying to convert people to his faith.
Reports said he was attacked in a busy street about 1km from his church.
"I hope this has nothing to with Islamic fundamentalism," Monsignor Luigi Padovese, the apostolic vicar for Anatolia, told the Associated Press news agency .
"The climate has changed... it is the Catholic priests that are being targeted."
Father Andrea Santoro, an Italian, was shot dead in his church in the northern town of Trabzon in February.
A 16-year-old boy has been charged with the 60-year-old priest's death. Witnesses said the youth yelled "God is great" in Arabic before firing two bullets into Santoro's back.
Another priest, a Slovenian, was grabbed by the throat, thrown into a garden and received death threats during an attack in the port of Izmir, AP said.