Yes, all New Zealand visitors (those with New Zealand citizenship) must apply for a Kenya visa before entering the country.
Fortunately, Kenya's tourist authority has established a speedier and easier way to get a visa. The Kenya electronic visa (commonly known as an eVisa) is available to New Zealand nationals. The most excellent aspect about this new visa is that you can apply online: it just takes one hour to apply, and you don't have to gather paperwork, stand in line at the embassy, or interview a visa officer.
Kenya eVisa is suitable for a single journey of up to three months. The Kenya tourist visa can be extended once for an extra three months. To do so, New Zealand passport holders must renew their Kenya eVisa in person at the Nairobi Immigration Headquarters.
New Zealand citizens must wait 2 to 3 days for the e-Visa to be processed after submitting their application. It is suggested that applicants allow more time than this, as unforeseen delays might occur, especially during busy seasons such as vacations.