Jamie Johnstone, 21, from Cranhill, died after being found with serious injuries in Balbeggie Street, Sandyhills, on 16 January.
Police have confirmed that a 25-year-old man has been arrested and is being detained in connection with the incident.
Nico Donnelly has already been charged with the murder of Mr Johnstone.
He made no plea or declaration during a private hearing at Glasgow Sheriff Court on Monday.
The 22-year-old, from Cambuslang, was remanded in custody.
A second man has been arrested following the death of a man outside a block of flats in Glasgow.