SA Chief Inspector Mark Collise said a man produced a knife when he was spoken to by staff at the store on Reid Street in Gawler, about 44km north of Adelaide, about 9.20am.
Police were called while supermarket management evacuated the store.
Police arrived within four minutes of being called and “discovered a man laying on the floor of the supermarket holding a knife”, Collise said.
He said the 50-year-old man was arrested without anyone being harmed.
Police have reviewed CCTV and discovered ”the man had very little interaction with anyone leading up the incident”.
Collise praised the actions of staff.
The man been taken to hospital where he is undergoing a medical assessment.