The artwork, showing Christchurch murderer Helen Milner - dubbed the Black Widow - is one of 49 on display at the Wallace Arts Centre in Auckland.
The family of the killer's victim say the piece "idolises" the woman who poisoned husband Philip Nesbit in 2009, and her son has questioned its validity.
Black Widow by Wanganui artist Mark Rayner is described as "hand hooked rug wool on rug canvas" and was judged one of the top 49 of 524 entries for the annual Wallace Art Awards, which "aim to support, promote and expose New Zealand contemporary art and artists".
Milner, 50, was found guilty by a jury in December of murdering her 47-year-old second husband by poisoning him with the allergy drug Phenergan and sentenced to jail for at least 17 years.
"I'm just shocked ... blown away," Mr Nisbet's sister Lee-Anne Cartier said from her home in Queensland.
"I can understand that artists want to capture both the good and the bad, but this is just distasteful."
Milner's son Adam Kearns also expressed concern over the use of his mother's image. "It doesn't sit real well with me," he said. "I just wish she'd go away. When's it all going to end?"
But UK-born Rayner has a history with controversial New Zealand figures - in 2009 he and brother Paul presented an exhibition of ceramic teapots with sweater-like tea cosies and David Bain-head lids.
While the Milner piece has angered both families involved, Wallace Arts Trust administration manager Matthew Wood said the artwork was worthy of display.
"We've had people coming in and asking why it's on display and saying it's particularly offensive in a way. [But] art doesn't necessarily have to be pleasing. That's an interesting process in itself."
Black Widow was not one of the seven major Wallace award winners.
Artist says sorry
Speaking from London, Mr Rayner this morning apologised to the families and explained his reason behind creating the piece.
He was very sorry to hear the families considered his intention was to "idolise the convicted killer ... or trivialise the tragedy behind this case".
"This was certainly not my intention and I apologise for any upset that this work might have caused for them."
The piece was, however, designed to be "unsettling" for those who viewed it, he said.
"I have deliberately chosen a well-documented media image which, to my mind, shows the subject in the most chilling light, staring directly at the viewer.
"But this work is not specifically about Helen Milner per se, it's more about the response of the viewer to a recognisable, disturbing image rendered in an unlikely 'craft' medium.
"I don't have any qualms about depicting a convicted killer in an artwork," he said.
The artwork took about 60 hours to complete, Rayner said.
Milner is intending to take her case to the Supreme Court after the Court of Appeal rejected her appeal against conviction.
Is it art?
Other controversial works:
• Mongrel Mob member Shane Harrison - accused of killing Sio Matalasi in Wellington last year - was featured in a exhibition by photographer Jono Rotman at Auckland's Gow Langsford Gallery in April.
• In 2010, a large portrait by artist Liam Gerrard of Clayton Weatherston, who murdered Sophie Elliott in 2008, was announced as a finalist in the Adam Portraiture Awards before being withdrawn.
• A Wallace Award winner in 2008, Richard Lewer's Skill, Discipline, Training, depicted references to Texan serial killer Richard Ramirez, dubbed the Night Stalker.
