Glen Nicolaides from London Fire Brigade told the BBC the whale had been moved to a more “stable” location where it would be assessed to determine the scale of its injuries and whether it could be released.
Earlier, a witness told the PA news agency that “quite the crowd” watched as the attempted rescue took place.
Jake Manketo, 20, from Richmond, said: “Everyone here is just hoping they get it out.
“We couldn’t believe our eyes when we first saw the poor fella, not every day something like this happens in Richmond.”
It is believed the whale was first spotted at midday a few miles up the river near Barnes Bridge.
Spotted in the River Thames at Barnes Bridge this morning. Is this a dolphin? #thames #dolphin #london #wildlife https://t.co/viaM6R6RGT
A spokesman for the PLA, which owns and operates the lock, said: “At around 7pm on Sunday, a small whale, approximately 3-4m long, believed to be a Minke whale became stranded at Richmond Lock and Weir.
“PLA staff have attempted to assist the whale with water along with British Divers Marine Life Rescue.”
Minke whales are the smallest of the great whales, growing to about 10m.
They can usually be found throughout the northern Atlantic and Pacific Oceans.
Their range extends from the ice edge in the Arctic during the summer to near the equator during winter.
The lock is situated between Teddington and Richmond, comprising of three vertical steel gates suspended from a footbridge.