The diagnosis was the first case in the South Island and the eighth in New Zealand.
"We are of course very stressed and worried about the well-being of our family at this point, but we are going to find the bright, brave and big smile for the sake of our children!" Kessler posted on the family's Instagram account.
Kessler added that neither himself or his family have experienced any symptoms of Covid-19 at this stage.
Kessler competed as a boxing professional from 1998-2013, claiming the WBA super-middleweight crown three times and finishing with a record of 46 wins from 49 fights, 35 by way of knock out. Kessler defeated former NRL star Anthony Mundine by unanimous decision in Sydney in 2005 to defend his WBA belt.
The family, along with the film crew they were travelling with, are now all in isolation in Queenstown while the woman diagnosed with the virus is reported to be recovering well.
The diagnosis came on the same day the Danish government recommended all Danes return to their home country, a fact that Kessler said made him "terribly sad".
Director-general of Health Dr Ashley Bloomfield told NZME public health staff were carrying out "contact tracing" on the infected woman's flights, and were requesting close contacts to stay in self-isolation for 14 days from the date of potential exposure.
