The unusually destructive tornado, which struck Thursday, also uprooted trees, damaged buildings and caused flooding that closed roads.
Two of the victims were killed when the tornado tore concrete slabs from a building and dropped them onto a truck in which the victims were traveling in. The third was reportedly killed by a falling tree.
Seven people were transported to local hospitals suffering from a range of different injuries.
Officials say the destructive tornado was the deadliest in more than 60 years. New Zealand isn't prone to large tornados despite reporting an average of seven tornadoes a year.