The medicine costs parents between $50 and $100 and is not part of the national immunisation schedule. Demand for the main Varilrix vaccine jumped in the past 12 months, with a 37 per cent increase in sales on this time last year.
Meanwhile, reports of "pox parties" being held by some parents keen to build their children's immunity to the virus have been slammed by the medical fraternity.
Dr Tuck advised against the practice, warning that chickenpox was a "nasty disease". "The sooner the vaccination becomes part of the routine schedule the better," he said.
"Introduction in other countries has shown not only that children don't need to get this miserable disease, but significant economic benefits to the country [result] by keeping parents at work."
Rochelle Gribble, editor of parent advice website kiwifamilies.co.nz, said immunising against chickenpox was still a contentious issue for some parents.
She confirmed some parents were even sending healthy kids to pox parties, where they could be exposed to chickenpox by a sick child.
Children infected with the virus were less likely to get it later in life when it could be more harmful.
The Immunisation Advisory Centre said cases of the virus normally peaked at the beginning of winter.
"It's a contagious disease and kids are spending more time indoors, mixing with each other and coughing and spluttering," centre medical adviser and paediatrician Marguerite Dalton said.
A shortage of the Varilrix vaccine was a good sign, she said.
"We've finally got the message through to people that there is a vaccine and it's really effective."
Side-effects from vaccination were relatively minor, compared to ailments associated with the disease. "If you have the chickenpox vaccine you might get a sore arm, but get chickenpox and you'll have a horrible high temperature, you're itchy and scratchy and you can't eat because your mouth's sore."
Public funding for chickenpox and rotavirus vaccinations are due to be reviewed this month by Pharmac, the Government's drug-buying agency.
Chickenpox
Small itchy blisters on the skin.
Symptoms: tiredness, fever, aches and pains.
Usually clears up within 3-7 days.
Rare but serious complications include pneumonia and problems with kidneys, heart, joints and nervous system.
Serious for pregnant women.
Source: Ministry of Health