The six-foot blue shark was spotted in shallow water in the River Fal between Falmouth and Truro on Wednesday.
Experts fear it could be injured or stressed, and should be "given a wide berth".
The shark could be disorientated, which might explain why it found itself in the Cornish river.
Blue sharks are one of several species known to migrate to the west Cornwall coast from the Atlantic in summer.
A blue shark
Wiki Commons
Cornwall's River Fal, where the shark was spotted
Wiki Commons
Staff at the British Divers Marine Life Rescue charity are monitoring its condition closely.
Dan Jarvis, speaking on behalf of the charity, said: "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 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."
It comes after dog walker Harry Gooby filmed the shark, saying it appeared to be trying to make its way onto shore.
He told The Telegraph: "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."