The man's body was found by a member of the public in Cadzow Street, near to Blythswood Court, at around 1.30am yesterday.
Police said the death of the man, thought to be in his 30s, is being treated as suspicious.
Officers cordoned off the site, from Argyle Street to the gates of the Cadogan Square Car Park.
An incident tent was set up nearby while both uniformed and plain clothes police combed the area.
So far, police have not released the man's name. The area is home to residential flats, including two high-rise blocks, as well as businesses.
Locals yesterday spoke of their shock at learning of the suspicious death on their doorstep.
A Police Scotland spokeswoman said: "The death is being treated as suspicious."