Hairdresser Tony Moore, 29, claims Father Frank King of St Aidan's church in Wishaw, Lanarkshire bombarded Mr Moore with 'inappropriate' messages.
"When he first added me on Facebook I wasn't really sure who he was," said Tony Moore to the Herald Scotland.
"He sent me a couple of messages just asking how I was which I replied to just to be polite.
"But then I got a message from him asking me to come to his house to have a drink. I thought it was a bit strange and I didn't reply.
"I found it really creepy and I couldn't believe I was being pestered like this by a priest. I had given absolutely no indication that I was interested in meeting up with him."
The Bishop of Motherwell, Bishop Joseph Toal reportedly held a meeting with Tony Moore and some family members last week, where he reviewed the messages Father King had been sending Mr Moore.
It's reported the matter was not referred to police and the priest has been asked to exercise care when using social media.
Parishioners informed that Fr King would not be conducting services when they attended Mass at the weekend. It's unclear when he will return.
Premier has contacted the Diocese of Motherwell and is waiting for a response.
