Police are concerned for the welfare of Westbury man Geoffrey Frank Trezise.
The 85-year-old former GP was last seen in Westbury about 8am on Monday.
Mr Trezise is described as being about 170 centimetres tall, of a slim build, with short wavy grey hair, hazel eyes and glasses.
He was last seen wearing light coloured trousers and a brown jumper.
Mr Trezise is likely travelling in a silver 2001 Alfa Romeo 166 registration number C86EE, police say.
It is believed he may be in the state's north.
Anyone who has seen Mr Trezise or his vehicle is asked to contact Tasmania Police on 13 14 44.