Officers raced to the scene in Langbar Crescent, Easterhouse, after a 22-year-old was assaulted.
It is understood the victim was in the street at around 11.30am when the attack took place.
Witnesses have been urged to come forward.
A block of flats in the street remained cordoned off yesterday evening.
A Police Scotland spokeswoman said: "We were called to a report of a 22-year-old man being assaulted at around 11.30pm on Wednesday.
"Officers attended the scene and the man was taken to Glasgow Royal Infirmary.
"Inquiries are ongoing."