They had taken a charter flight home to Auckland on September 11, after finishing their managed isolation period in Christchurch.
The Ministry of Health said the family visited the Taupō Tandem Skydiving base at Taupō Airport on September 19, between 2pm-3.30pm.
Taupō Tandem Skydiving chief executive Hamish Funnell said the skydiving instructor was wearing a face covering and a full-face helmet, and the tandem diver who later tested positive for Covid-19 was wearing a high-velocity-style face covering.
"As a precaution, the person he [the positive case] jumped with is considered a close contact and is in isolation for two weeks. Everybody else who was a casual contact in the aircraft is in isolation until they get a negative result."
"All tourism operators are struggling at the moment. New Zealand domestic tourists have been fantastic, it's not an ideal situation for us [to close], but it's the right thing to do."