Nash went on to suggest that a fellow inmate should scalp Smith.
"Scalping is associated with American Indians but it was actually started by Europeans.
"Perhaps someone in jail who isn't too fond of monsters who destroy little boys[sic] lives by stealing their innocence in the worst way possible could reintroduce Mr Smith to the practise[sic]."
Nash, who is the MP for Napier, later deleted the post.
He said his wife Sarah told him to remove it: "She said it probably wasn't the kind of statement an MP should be making."
Nash said he made the comments because he "loathed paedophiles", and because Smith was "at the bottom of the heap".
But he conceded that he "went a bit far" and that encouraging an inmate to harm Smith was "probably not prudent".
Smith is serving a life sentence for the 1995 murder of the father of a 12-year-old Wellington boy he had been molesting.
He escaped from prison in November 2014 and fled to Rio de Janeiro, using the toupee as a disguise.
When the hairpiece was taken from him for his subsequent court appearances, he said he felt "belittled, degraded and humiliated".
Corrections Minister Louise Upston said yesterday she was only concerned for Smith's victims.
"My view and my concern is actually for the victims of the prisoner concerned. His victims are the victims."
Labour candidates and MPs were recently told to "clean up" their social media profiles to remove any incriminating photographs or negative comments about the party.
Nash said he had not heard from the party about his Facebook comments.