Police were called to reports of a man armed with a screwdriver and shouting on Chelsea Bridge Road, in Chelsea, just after 09:00 BST on Saturday.
Officers challenged a man in his 40s before shooting him with a Taser. He then fell into the river.
The man is in a critical condition in hospital and an internal investigation has been launched by the Met Police.
A Met spokesman said shooting the man with a Taser "did not enable the officers to safely detain him" and he "subsequently entered the river".
He added: "A rescue operation was immediately organised.
"The man was rescued from the water by the RNLI and taken to hospital, where his condition has been assessed as critical."
Police are trying to reach the man's family to offer them support from specialist officers.
Meanwhile, the force's Directorate of Professional Standards is probing the circumstances and the Met has referred itself to the Independent Office for Police Conduct (IOPC).
Det Ch Insp Rory Wilkinson said: "My thoughts are with this man, who is extremely unwell in hospital.
"Officers are making every effort to make contact with his family.
"I understand that there are always concerns about incidents in which people come to harm having been in contact with police.
"All Met officers know that they are accountable for their actions, and a full investigation is under way to establish exactly what happened."
A spokeswoman for the IOPC confirmed an independent investigation is under way.
She said: "Investigators have been deployed to their post-incident procedure and the scene."