The six-foot blue shark was seen in shallow water in the River Fal between Truro and Falmouth. Experts have warned people to give the predator a “wide berth” amid fears it could be unwell, injured or disorientated.
Dan Jarvis, of the charity British Divers Marine Life Rescue, said his team was monitoring the shark.
He told the BBC: “This is a real worry for us because they don’t normally come up so close to beaches like this.
“Our worry is that it is injured or unwell and might need some medical attention.
“Our advice is to ignore it and give it a wide berth.
“It could be disorientated and it’s best for our team to monitor it, to give it the space and time to do what it wants.
“It could have just come for a look and will swim off when it’s happy to, but if it’s unwell we don’t want to cause it any more stress by people getting into the water and interfering with it.”
Harry Gooby was stunned to see the shark as he was walking his dog and filmed the sight.
He said: “I was waiting less than a minute when a shark swam very close to the shore and at one point put his snout up onto the beach.
“His whole head came out of the water and almost nuzzled the underneath of its neck on the beach.”
It comes after a snorkeler was bitten off the coast of Cornwall earlier this month during a diving trip to see blue sharks.
The incident was the first shark attack in Britain in 175 years.
The woman said afterwards: “I just wanted to say that, despite how the trip ended, it was amazing to see such majestic creatures in the wild and I don’t for a second want this freak event to tarnish the reputation of an already persecuted species.
“I wanted to thank everyone for their amazing actions.
“What was a very scary incident was made so much easier by the kindness and calmness of the people around me.
“Thank you to the trip team for getting me back to shore quickly and carefully and making me feel as safe as I possibly could.
“We all take these risks when we enter the habitat of a predator and we can never completely predict the actions of a wild animal.”
Blue sharks visit British seas in summer months and are generally spotted around 10 miles off the South West coast.
The largest blue shark ever caught in UK waters weighed 256lbs (116kg) and measured over 9ft (2.74m).