When UK Prime Minister Boris Johnson had Covid-19, Ardern sent him a text wishing him the best.
Asked if she had done the same for Trump, she said she had not as she does not have his personal phone number.
"Instead, we have used our official channels to pass on that message."
She plans to convey that sentiment in person, when she gets a chance to.
Ardern said New Zealand would wish anyone experiencing Covid-19 a speedy recovery – "and our very best wishes".
She said it was too early to say what the implication of Trump's diagnosis was for New Zealand.
"We still haven't seen out of the administration the likely effect they believe it will have on the election campaign."
She noted there had never been a time in US history that an election date had been moved.
"At this stage, I would say it would all be highly speculative – we just haven't had anything official from the White House in that regard."
Meanwhile, National Party leader Judith Collins also talked of Trump's health battle while in campaign mode in the Hawke's Bay.
"It happens to everybody if you come into contact with it - it's a highly contagious virus," Collins said.
"It doesn't seem very nice taking joy in anyone having that virus and I don't. I just think we'll see what happens but I'm sure he's getting the best care in the world.
"It shows you anybody can get it and it shows you again that it's a highly contagious virus.
"He's getting the best treatment, I see he's been shifted to a military hospital today where there's a presidential suite so he can continue to work. But I'll just say it happens to anybody - you've got to be careful."
When asked what his message for Trump and his family was, Collins said: "My message to anybody - and I don't take any joy in what's obviously quite a debilitating virus in some cases - I'll just say they'll be fine, like everyone else. I'm not someone who takes joy in someone else's sickness."
