Officers raced to Kenmure Street in the city’s Pollokshields at around 4pm on Monday after they received a report of a man with the weapon.
They were also informed of an alleged assault.
When the force arrived at the scene, they did not locate anyone who appeared to have been assaulted or injured.
A 44-year-old man and 43-year-old woman have been arrested in connection and an investigation has been launched into the exact nature of what happened.
A spokesperson for Police Scotland said: “Around 4.05pm on Monday, 6 May 2024 police received a report of a man brandishing a crossbow in Kenmure Street, Glasgow. There was also a report of someone having been assaulted.
“At this time police have not traced anyone who has been assaulted or injured.
“A 44-year-old man and 43-year-old woman have been arrested in connection with the incident.
“Enquiries are ongoing to establish the exact circumstances of the incident.”
