Three people were attacked on Sunday morning at East Street Market, near Walworth Road, south London, the Metropolitan Police said.
While one man died at the scene, two other people – a man and a woman – were taken to hospital for treatment.
A man, believed to be in his 60s, was arrested at the scene and taken into custody.
The incident is not being treated as terrorism.
Metropolitan Police Commander Peter Stevens said: “Tragically, a man lost his life this morning, and officers are working hard to establish exactly what happened and to provide support to his family. My thoughts and sincere sympathies are with them, and with the other people injured.
“Our investigation is at a very early stage. One man was rapidly arrested by officers responding to the incident. At present, although enquiries are ongoing, nobody else is sought.
“The incident is not being treated as terrorism. Enquiries continue, led by dedicated detectives from Specialist Crime.
“I want to thank those people who have already shared their accounts of what they saw with police. I urge anyone with information or footage, or any witnesses yet to speak with police, to get in touch.”
Witnesses or anyone with information have been asked to call 101 or message @MetCC on X, quoting reference 2690/10nov, or contact Crimestoppers if they wish to remain anonymous. By Kyriakos Petrakos, I News