The North Shore MP later added: "Don't be so precious, petal."
The Opposition side of the House erupted with calls for an apology, which the first-term Government member refused to give.
Labour MP Trevor Mallard later wrote on his Twitter feed: "Shame on Maggie Barry ... Women parliamentarians should know better than to criticise each other for not having children."
Other Twitter users have jumped on the comment, setting up a satirical thread called Maggie Barry's Standing Orders, with users making suggestions about other topics only some MPs should be able to comment on.
Suggestions included "No more references to Willie Apiata by MPs who haven't rescued comrades under enemy fire" and "only MPs who served in WW1/2 can vote to monday-ise ANZAC day".
Speaking after the debate, Ms Barry, who had her only child in her late 30s, said: "I am not apologising for it. I don't think it's a very sensitive issue. Jacinda dishes the dirt as much as any.
"When it comes to these things Jacinda Ardern is getting her knowledge from books as opposed to personal experience.
"When people take the moral high ground they probably are leaving themselves open a bit."
Ms Barry said there was still time for Ms Ardern to have children. "I didn't have my son Joe until I was 38. I don't know how old Jacinda is but there's still plenty of time for her to have kids."
Ms Ardern said she was not phased by Ms Barry's comment, but believed MPs should avoid making personal comments about each other.
"I try and avoid making personal jibes about politicians because you never know people's personal circumstances. She obviously doesn't have that rule, but I'm not going to take it to heart. I'm not expecting an apology either."
Ms Ardern said she rejected any insinuation that she was not qualified to talk about paid parental leave because she had no children.
"We all the time have to talk about issues we haven't personally experienced. I haven't been to Antarctica, but I know it's cold."
The parental-leave bill passed its first reading by one vote. National and Act opposed it. United Future's Peter Dunne cast the deciding vote.
The debate opened by Ms Moroney was punctuated by yells of "show us the money" from National MP Nick Smith.
Ms Barry said National was not arguing against the merits of paid parental leave, but the cost.
Her colleague Louise Upston, MP for Taupo, said that "in planet Labour, money seems to grow on trees".
Closing the debate, Ms Moroney said she hadn't been prepared for the "venom" that came from National.
"The sheer anger led by Dr Nick Smith and carried on by Maggie Barry was something I wasn't prepared for. To me it demonstrated an anger towards working families," she said.
"I thought it was quite ugly. This is coming from a government who were on the wrong side of the class-size issue," Ms Moroney said.
In April, Finance Minister Bill English said the Government would veto the bill because it would require an extra $500 million in borrowing over the next three to four years.
Ms Moroney obtained Department of Labour advice that showed the estimated cost was $285.6 million over three years. The costings showed that in three years, the full 26 weeks' parental leave would cost $315.6 million a year.
