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.

Jason Chung Yai-Ho, from Glasgow, was last seen in his inflatable red kayak off Traigh beach near Arisaig at about 16.30 on Wednesday.
He had set off despite an off-duty police officer warning him not to go out because of squally weather.
Two lifeboats, coastguard rescue teams and helicopter and police search dog teams have been involved in the search.
The helicopter search was stood down on Thursday night but coastal searches from Mallaig to Gortenachullish continued on Friday and Saturday.
Mr Chung Yai-Ho is 5ft 8in tall with short dark hair and a beard. He was last seen wearing a black waterproof jacket, black waterproof trousers and a black buoyancy aid.
His car, a red 2003 Toyota Corolla, was found parked near to the beach and has been recovered by the police.
A Police Scotland spokesman said: "Over the weekend there will be continued searches co-ordinated by police based in Fort William.
"Local officers will be supported by specialist search teams and dog units. Further assistance will be provided by HM Coastguard and the Lochaber mountain rescue team.
"If anyone has seen Jason or has any information regarding his current whereabouts or movements prior to when he was last seen on Traigh beach, they are urged to contact police on 101."

The Science Museum Group announced it would transfer the collection to the Victoria and Albert Museum.
It said the move will help create "the world's foremost single collection" on the art of photography and help the media museum focus on science and technology.
Bradford South MP Judith Cummins said she was "shocked" and "dismayed".
The transfer includes the Royal Photographic Society (RPS) archive, which features key historical objects from the medium's development.
Fewer than 10 items from the RPS collection are currently on permanent display in Bradford but the majority can be viewed by appointment.
The archive will join the V&A's existing collection of 500,000 photographs to create an International Photography Resource Centre.
Bradford will retain the Kodak collection, the Daily Herald Archive and the Impressions Gallery.
Jo Quinton-Tulloch, director of the media museum, said it would focus on inspiring future generations of scientists and engineers in the fields of light and sound.
She added: "We retain millions of objects in our photography, cinematography and television collections which will help us make these scientific principles tangible and exciting."
The media museum currently holds more than 3.5 million items, including the world's earliest known surviving photographic negative, the earliest television footage and the camera that filmed the first moving pictures in Britain.
It was under threat of closure in 2013 and visitor numbers have fallen from a peak of nearly a million in 2001.
Ms Cummins said: "We need to make sure this isn't cuts or closure by stealth.
"I want to see the museum stay in the city, it's a national museum and it needs to stay where it belongs - in Bradford."
A pensioner from south Wales is at the centre of a police hunt after vanishing during a coach holiday to the Isle of Wight.
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Searches are continuing for a kayaker missing in the Highlands for three days.
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A 400,000-strong photography archive is to be moved from Bradford's National Media Museum to London.