Senior Sergeant Anthony Bond, of Dunedin, said police were called to Vapourium in London St at 4.30am after an alarm was activated.
When police arrived, they saw the shop window was broken and vape products were found on the ground outside the store.
Police investigated and dogs were brought in to try and track the burglars, however, they were unable to locate anybody.
That meant they most likely left in a vehicle, Snr Sgt Bond said.
The investigation was handed over the the Criminal Investigation Branch for further investigation, but there are no suspects at this time.