Police called to The Street on the ground floor of the centre at 16:25 BST said several males were involved.
Two others have also been stabbed. All victims are thought to be in their late teens or early 20s.
Five men, aged between 20 and 23, have been arrested in connection with the killing and are being held in custody, police said.
London Ambulance Service said it treated one man for stab wounds and another for minor injuries.
It is understood both injured men were taken to hospital from Stratford Underground station, however it is not clear where their injuries happened.
Acting Detective Chief Inspector Andy Kelly said: “We believe that shoppers at the centre may have filmed or photographed some part of the incident on their mobile phones.
“We encourage them to come forward and share this potentially vital material with us.”
A spokesman from the shopping centre said: “Westfield can confirm an incident occurred this afternoon at Westfield Stratford City.
“Westfield is working closely with the police and emergency services, however as this is a police matter we cannot provide any further details at this stage.”