Police were called to reports of a disturbance in a flat in Benalder Street, Partick, at 8.50am yesterday and found a 29-year-old man seriously injured.
He was treated by paramedics but died at the scene.
Officers described the death as “suspicious” and launched an investigation.
A 23-year-old man has now been arrested in connection with the death.
A report will be sent to the procurator fiscal and the man is due to appear at Glasgow Sheriff Court on Monday.
Police said a 25-year-old woman was also injured in the incident and is being treated at Glasgow’s Western Infirmary.
The incident took place in the flat above The Dolphin pub.
Owner Stephen McBride said: “All I know is that there has been an incident upstairs.
“When I turned up I was told by Police it was a major incident.
“I saw someone being put into the back of an ambulance.
“They are still going through my CCTV.”
One man, who wished not to be named, said: “When I arrived at 9.30am there was a lot of police and two ambulances.
“I saw a guy being escorted into a police vehicle. He wasn’t handcuffed.
“There was lots of flashing lights and a lot of people stopping to have a look.”
Another man, who did not wished to be named said: “All I know is that someone has died.
“I started work at 7.30am and never heard anything till the police turned up.
“Nobody seems to know what has happened.”