Police are still not confirming how many people have been arrested in connection with the alleged murder in Great Linford.
Details of the victim have also not been released.
Meanwhile it is understood a second person was injured in the alleged incident.
The area around the Co-op in St Leger drive is still cordoned off and the store remains closed.
Over the weekend a forensic tent was in place between the Co-op and the former Pilgrims Bottle pub.
Police launched a murder investigation after officers were called to St Leger Drive at around 4am on Saturday,
“Officers attending the scene found a deceased man,” said a police spokesman.
Formal identification has not yet taken place.
A post-mortem is taking place this week to discover the cause of death
Senior investigating officer, Detective Chief Inspector Craig Kirby, of Major Crime Unit, said: “At this stage we believe this was an isolated incident, there is no danger to the wider public, and arrests have been made in connection with the incident.
“We have a number of scene watches in place in Milton Keynes whilst we continue to investigate.
Superintendent Yvette Hitch, said: “I am aware that this will be very worrying and shocking for the local community in Great Linford.
“In light of this we are increasing patrols in the area to provide reassurance to the community, and you may see an increased police presence over the coming days.
“If anyone is concerned about this incident we would advise them to please speak to one of our neighbourhood officers.”