One woman asked if the officers were single; another said "I'll take all four thanks".
It was also suggested the officers should make a dog handler calendar.
The photo had more than 340 likes and 110 comments as of 8.30am today.
It's not the first time Mauheni has been in the spotlight.
In 2013, Mauheni and his police dog, Thor, were awarded the Erridge Cup for being New Zealand's best-performing rookie dog and handler in the previous year.
In March this year, he was one of the four police officers injured during a siege at Kawerau.
He was allegedly shot in the head by Rhys Warren during a cannabis recovery operation. He received a brain injury and spent time recovering at home.