Police were called to an incident in Islip Gardens, Northolt, on 28 June and arrested the pensioner on suspicion of possession of an offensive weapon and criminal damage to a motor vehicle.
One officer "discharged a Taser" during the incident, the Independent Police Complaints Commission (IPCC) said.
The man was taken to hospital after he complained of pain while in custody.
Inquiry starts
Police were responding to reports of a man being threatened in Ealing borough, following which they arrested the pensioner.
The 82-year-old, who was at Acton police station after being arrested, was taken to Central Middlesex Hospital by an ambulance when he complained of pain.
The pensioner, who has since been discharged, was in hospital for several days, the IPCC said.
The IPCC has begun an inquiry.
IPCC Commissioner Rachel Cerfontyne said: "Our investigation will examine whether the use of a Taser in these circumstances was proportionate and appropriate."
My guess is probably not...