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