A video posted to social media showed a male with long hair, dressed only in underwear, being led in handcuffs in to the back of a police van.
Scotland Yard said in a statement: "Police were called at 11.06am on Wednesday, 19 December to reports of a stabbing at a health centre on St Stephen's Road, Tower Hamlets.
"Officers, including specialist firearms officers, attended and found three people suffering from stab injuries.
"They were taken to hospital; their injuries are not being treated as life-threatening.
"A man was detained nearby and taken to hospital suffering from an injury."