The Dunedin-based National list MP posted a series of photographs taken at the New Zealand Association of Migration and Investment conference in Auckland on Saturday.
While most of the comments in response to the post were positive, Londoner Mark Lambert took exception to the minister's approach to immigration.
"Here's a question n answer in one, when are we going to get tough n say no more immigrants? And if yr answer is why then you need to go to specsavers, then remove yr self from my page ... [sic],'' he posted.
Mr Woodhouse snapped back, pointing out Mr Lambert had in fact posted on his Facebook page.
"I think you'll find you're on my page you redneck,'' he replied.
Undeterred, Mr Lambert became more abusive and said ``hope I get to meet you real soon''.
Mr Woodhouse replied that an encounter was doubtful due to some restrictions on immigration in New Zealand.
"Mark Lambert, unlikely, NZ has a strict no dickheads rule,'' he quipped.
Mr Lambert still appeared confused about whose page he was on, saying in another abuse-laden message "I will remove yous lot of my fb page do gooders [sic]''.
Mr Lambert had posted messages of support for Brexit on his own page and declared his support of Chelsea's football team - to which his views on immigration apparently do not extend, as 66% of its squad represent nations other than England.
When contacted yesterday, Mr Woodhouse did not want to comment further on the exchange.
