Police received a call about the break-in at the supermarket on Ossian St just before 1am on Wednesday.
"It appears those involved gained entry to the store and attempted to take an ATM by utilising a vehicle but were unsuccessful," a police spokeswoman said.
"Those involved left the scene and were unable to be located by police at the time.
"Police are investigating the incident and making inquiries to locate those involved."
The owner of the Four Square declined to comment at this stage.
Tradespeople were at the Four Square on Wednesday working to repair the front entrance and the store remained open with customers using a separate door.
The large security wall at the front of the store had been completely toppled over, with visible damage, from what looked to be a forceful impact.
It was resting on top of the trolleys in the foyer of the store.
An ATM in the foyer area was visible from the street but appeared to be undamaged.
Another glass wall between the foyer and the actual store also appeared to be undamaged.
Eastern District Police acting area commander Inspector Martin James said these crimes would not be tolerated.
"Police are committed to addressing ram raid style burglaries and other types of retail crime in communities," he said.
"We understand this type of offending is extremely frustrating for business owners, who suffer losses and damage to their business, and which can be disheartening and frightening for staff.
"Police are actively seeking to locate the people involved in the incident in Ahuriri [on Tuesday] night and intend to hold them accountable for their actions."
In response to retail offending across New Zealand, police have set-up the National Retail Investigation Support Unit to help stop repeat offending and work with businesses.
A staff member, who did not want to be named, at Cafe Ahuriri across the road from the supermarket said they had been broken into twice in the past six months, including last Monday.
She said nothing was stolen in the latest break-in but the doors had been damaged.
She said the break-ins happen at night and there was no trouble during the day.
She said prior to those incidents it had been a long time since they had seen any break-ins.
At the end of May, the Meeanee Hotel just outside of Napier was also ram raided and an ATM was stolen.
Police have since arrested and charged two people over that incident.
