Michael Davies, 71, had been staying at a hotel with his wife at the holiday resort when he disappeared.
The couple, from Blaina, Blaenau Gwent, had travelled to Sandown on the island by coach, Hampshire Constabulary said.
But Mr Davies, who suffers from high blood pressure, has not been seen since the early hours of Wednesday.
The force said Mr Davies wandered off after dinner at the Hotel Maria in Sandown at 21:30 BST and CCTV images later show the him less than half a mile inland from the seaside hotel.
A police spokesman said: "We are growing increasingly concerned for the welfare of a 71-year-old man.
"Having reviewed CCTV it appears that Michael was in the Avenue Road area of Sandown just before 01:00 on Wednesday morning."
Police said the pensioner's family were worried because Mr Davies relies on medication to control his blood pressure, which he would not have access to.
He is described as white, with cropped white hair, and wearing a blue tee-shirt, blue Reebok jumper, jeans and a baseball cap.
A pensioner from south Wales is at the centre of a police hunt after vanishing during a coach holiday to the Isle of Wight.