"Wishing the PM a quick recovery from Covid and that she can join us in parliament again soon."
The National Party leader had his own bout with Covid-19 in March.
Ardern's daughter Neve tested positive on Wednesday, the PM said in her Instagram post.
"Despite best efforts, unfortunately I've joined the rest of my family and have tested positive for Covid-19," she said.
"To anyone else out there, isolating or dealing with Covid, I hope you take good care of yourselves!"
The Prime Minister will be required to isolate until the morning of Saturday, May 21.
She will not be in Parliament this week for the release of the Government's Emissions Reduction Plan this Monday or for the Budget on Thursday.
Travel arrangements for her trade mission to the United States are unaffected at this stage.
The Prime Minister will undertake what duties she can remotely this week, but Deputy Prime Minister Grant Robertson will take the post-Cabinet press conference on Monday, May 16.
"This is a milestone week for the Government and I'm gutted I can't be there for it," Ardern said.
"Our emissions reduction plan sets the path to achieve our carbon zero goal and the Budget addresses the long-term future and security of New Zealand's health system.
"But as I said earlier in the week, isolating with Covid-19 is a very Kiwi experience this year and my family is no different."
The country first learned of the Prime Minister's close contact with Covid-19 after she announced Gayford's positive test in an Instagram post to mark Mother's Day.
Below a photo of a sweet card from daughter Neve, 3, Ardern wrote that Gayford had woken feeling "a bit average" before testing positive.
"So we have 7 days of family time ahead of us!"
The Prime Minister is far from alone - more than a million Kiwis have tested positive for the virus since the pandemic began, although experts think the actual number of infections is double that number.
Among them are a slew of fellow politicians, including Luxon and Covid-19 Response Minister Chris Hipkins in March.
Former National leader Simon Bridges, Police Minister Poto Williams and MPs Tamati Coffey, Anahilia Kanongata'a-Suisuiki, Joseph Mooney, Penny Simmonds and Stuart Smith have also previously tested positive for Covid-19.
Environment Minister David Parker was the first New Zealand MP to test positive for the virus.
Internationally, Ardern may be one of the last leaders to remain Covid-free until today.
Many world leaders having been infected over the past two years, including former US President Donald Trump and current British Prime Minister Boris Johnson, both of whom were hospitalised with the virus in 2020.
Australian Prime Minister Scott Morrison, French President Emmanuel Macron, Canadian Prime Minister Justin Trudeau and Brazilian President Jair Bolsonaro have also previously tested positive.
The presidents of Mexico, Poland and Pakistan have all twice caught the virus.
Royalty also haven't been spared: the Queen, Prince Charles (twice), Prince William
and Camilla, Duchess of Cornwall have been among the 520 million cases worldwide.
