Zika virus is a flavivirus, closely related to dengue. Although outbreaks of Zika virus have previously been reported in tropical Africa and Southeast Asia, there have been more recent cases reported in the Pacific Islands. The mosquitoes that are able to transmit Zika virus are not normally found in New Zealand, so you should only be concerned if travelling overseas. Zika virus infection is symptomatic in only about one of every five cases and when symptomatic the infection presents as an influenza-like syndrome (low-grader fever, headaches, myalgia etc).
There are however more concerns that pregnant women who become infected with Zika virus can transmit the disease to their unborn babies, with potentially serious consequences. Until more is known, the Ministry of Health recommends that women who are pregnant or plan to become pregnant in the near term consider delaying travel to areas with Zika present.
If you would further information please check the MOH website http://www.health.govt.nz/our-work/diseases-and-conditions/zika-virus