"We have seen now several world leaders who are being affected by Covid-19 and I know that I stand with others in wishing all the best," she told reporters this afternoon.
"This is, obviously, a virus that has had a devastating impact."
She has asked her officials at the New Zealand Embassy in the US to pass along a message, wishing "the President a speedy recovery on behalf of New Zealand".
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.
Ardern said that 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 that there has never been a time in US history that an election date has 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."
The Labour leader was one of the first New Zealanders to vote in the 2020 election this morning – casting her ballot just hours after early voting began.
Her vote was "two ticks Labour," she told reporters who were invited along to witness her cast her vote.
She was joined by her fiancé Clarke Gayford, who also voted for Labour and Ardern - she is the local candidate in Mt Albert.
"He didn't get a choice," Ardern joked as the pair left the voting station.
She arrived with Gayford just after 11am and spent about two minutes in the voting booth.
There were only a few other voters at the centre this morning - two who passed Ardern on their way out both said they had voted for her.
"Oh, thank you," she replied.
Although she said he had voted for Labour, she did not reveal how she voted in both the referendums.
She will now speak at Labour's Get Out The Vote event, where she encouraged people to cast their ballot early.
Early voting officially opens across the country today and the take-up is expected to be higher than ever.
