A taxi driver has had his cab stolen at gunpoint outside Adelaide's Queen Elizabeth Hospital.

Police said the hijacker was armed with a sawn-off shotgun when he took the car shortly before 11:00pm.

The vehicle was fitted with a GPS tracking device and police chased it through backstreets at Lockleys before the driver stopped on Noble Street, where he was arrested.

Officers searched the taxi and found a double-barrelled sawn-off shotgun.

Police charged a 23-year-old man from Woodville West with robbery, and firearms and driving offences.

The man allegedly recorded a blood alcohol reading of 0.143 per cent.

He was refused bail and will appear in the Port Adelaide Magistrates Court on Monday.