A 57-year-old man has been fatally shot after police responded to reports of two men arguing in Summers Street.
Police have cordoned off the street and forensic experts are on the scene.
The force says it has referred itself to the Independent Office for Police Conduct.
A IOPC spokesperson said: “The Independent Office for Police Conduct has begun an independent investigation following an incident involving officers from Wiltshire Police in Summers Street, Swindon at just after 2am on 8 November.
“At this early stage it is believed a 57-year-old man has been fatally shot during the police response to reports of two men arguing in the street.
“He was declared dead in an ambulance at 2.56am.
“Our thoughts and sympathies are with all of those affected by this terrible incident.
IOPC investigators are at the scene, and the post incident procedures where the key police witnesses will provide their initial accounts.”
A Wiltshire Police spokesman said: “We can confirm that following an incident in Summers Street, Swindon, shortly after 2am this morning a referral has been made to the Independent Office for Police Conduct.
“This is regarding the death of a member of the public.
“The IOPC are independently investigating this incident so it would be inappropriate for us to comment any further on it.
“We would, however, like to reassure the public there is no risk to the wider community and that there is likely to be an increased police presence in the area for a considerable time.”
The IOPC statement added: “It is mandatory for us to conduct an independent investigation when the police fatally shoot a member of the public. We have established protocols with the police to ensure our investigations do not hinder their ability to conduct enquiries as part of their related investigations.”