The mammal, measuring between three and four metres long, was spotted beached at Richmond Lock at around 7pm on Sunday.
By 9pm a crowd of around 200 people had gathered to watch as lockkeeping staff sprayed the whale with water using a hose.
Medics from the British Divers Marine Life Rescue and the Fire Brigade also attended the scene to try and assist the animal back into the river.
Martin Garside from the Port of London Authority, which operates Richmond Lock, said he believed it was furthest a whale had ever swum up the Thames.
"It's 90 miles from the North Sea - that's quite an achievement," he told The Independent. "No whale has ever swum this far".
The mammal was first spotted on Sunday lunchtime by filmmaker Gareth Fubry near Barnes Bridge.
"We couldn't tell what it was at first - perhaps a dolphin, porpoise or whale," said Mr Garside.
"There were no other sightings until about 7pm when Port of London Authority staff found what we believe to be a small minke whale beached just underneath the footbridge at Richmond Lock."
As a large number of spectators arrived to see the mammal, the Metropolitan Police attended to manage the crowd and keep people away from the whale.
"Too many humans near an animal stresses them out," said Mr Garside. "And it must be stressed already."
Video footage and photographs on social media showed rescuers trying to help the whale, which appeared to be stuck on the lock’s boat rollers.
In 2019 three whales were found dead in the River Thames, including a humpback whale nicknamed Hessy.
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