Constable Mike Johnston said the man was arrested but was not likely to face any charges at this time because he was clearly unwell.
The phone call was made anonymously and the caller had said the bomb was "going to go off now", Const Johnston said.
The incident sparked an orderly evacuation of the supermarket and some nearby businesses on Dunmore St for two hours.
Part of Dunmore St was also cordoned off.
Police investigated the call and found the man at home about 2km from the store, smashing up his property.
The police took the man to the supermarket to get him to indicate where he said the bomb had been placed.
The investigation by police, fire officers and an electrician centred around the shop's freezers as well as the refrigeration units out the back.
No explosive device was found.
A Dunedin-based police bomb squad and police dog was on stand-by but was stood down.
Const Johnston said the police had enough information early in the investigation to make a judgement about how to deal with the situation but they had to treat the incident seriously and clear the store as quickly as possible because they did not know what they were dealing with.
Wanaka's police officers had all trained and worked in cities and were familiar with bomb procedures, Const Johnston said.
If any device had been found in the supermarket, the army would have been called in to deal with it.
Const Johnston believed the cordoned-off area was large enough to contain the situation.
The incident is believed to be Wanaka's first bomb scare.
Supermarket workers were instructed not to comment yesterday but it is understood the incident resulted in the destruction of a lot of frozen goods.
Many shoppers returned to the supermarket shortly after 3pm to discover their abandoned trolleys had been taken away and they had to start again.
It is understood the supermarket was not particularly busy when the bomb report was made, with only about 20 shoppers in the store.
Store manager Chris Wilson said all the staff were "fine".
"Everyone performed to their best in the requirement for an evacuation," Mr Wilson said, before referring all further requests for comment to police.
Community worker Wendy Mitchell was one of the hundreds of people who had their midday plans disrupted by the false alarm.
But in the end, Mrs Mitchell, who was evacuated from her office in Dunmore St, could not help but laugh.
Neither could other bystanders and soon, quips began flowing thick and fast about the seemingly relaxed and calm attitude displayed by emergency services.
Whether the evacuation and street cordon was far enough away for public safety was a keenly debated subject.
Just down the road, people continued to drink coffee at pavement tables, seemingly oblivious to the drama just a block away from where they sat.
