Counties Manukau South Area Commander Inspector Dave Glossop said the fires were "very concerning".
"We have put together an investigation team and are working closely with Fire and Emergency New Zealand. We want to assure our community that we are following positive lines of enquiry but would like anyone who recognises the person in these images to contact police immediately.
"While the photo does not show the suspect's face, we believe that someone may recognise the clothing and build of the offender," said Glossop.
"We estimate the total damage to the properties to be in the hundreds of thousands of dollars, if not higher. We have brought in extra resources and our staff are actively patrolling high-risk areas. We urge our community to contact 111 immediately if they notice any suspicious activity particularly in the Counties Manukau South area from Papakura to Pukekohe."