The alleged incident occurred in Dunfermline, Fife, while the ambulance was on a response call to take a patient to hospital.
An ambulance worker, who did not want to be named, said a life could have been at stake.
The worker said: "It's something you do not do. As soon as you ... leave the station you go to that address. You don't go via shops. They stopped at PC World on the way to a doctor's urgent call."
The Scottish Ambulance Service confirmed that the incident had happened, but would not provide any more details.
A spokesman said: "We are investigating an instance of unauthorised diversion during a non-emergency call. Patient care was not affected, but it did not meet our high standards."