Warner says Zoe is too young to raise a disabled child and that it will "crush her".
"Zoe's not a stay at home person at the best of times, now she'll be chained at home forever."
Kim Porthouse, spokesperson for The New Zealand Down Syndrome Association, said the group is "appalled by the insensitive and ignorant storylines".
Porthouse said the storyline "reinforces a lot of the prejudice that having a child with Down syndrome is a burden".
Porthouse said the organisation has received calls from a number of families and people with Down syndrome who have been upset by the episodes.
"But what is worse is that a lot of our young people with Down syndrome absolutely love Shortland Street and suddenly one of their heroes tells them their families would have been better of without them," she said.
Porthouse said the issue of screening is a sensitive issue and many women are not made aware of it. Those that do receive a positive test are often not given balanced information.
"These parents are put under a lot of pressure to make only one choice, to abort, and the statements by Dr Warner on Shortland Street just emphasise that."
However, the storyline has seen characters discuss Zoe's options with her.
Chris Warner's adult son Finn stresses the choice is hers and that she will have support no matter what options she chooses.
"You don't have to do anything you don't want to do, there's thousands of stories out there, mums and dads who have been exactly where you are and they've kept their baby," he tells her.
Kate also advocates for Zoe making her own choices about testing and continuing the pregnancy.
In a joint statement, TVNZ and South Pacific Pictures said they acknowledge the storyline addresses a sensitive topic but Shortland Street is known for tackling a range of challenging issues that New Zealanders face.
"The show's producers work closely with medical advisors to ensure health storylines are depicted with care in the context of a drama.
"We realise that not everyone will agree with every choice we make, but we always appreciate when people come to us to share their feedback. We consider the full range of the audience views when making future decisions."