The 33-year-old victim was walking on Bankhall Street, Govanhill, when a youth ran up and stole his phone.
Police said the suspect then made off and ran into a common close but was followed by the victim.
The victim was then threatened by the suspect and two other men in the close before they ran off with a four-figure sum of cash. It happened at around 5.45pm on Friday.
Detective Constable Alister Thom appealed for any witnesses to come forward. Contact Pollok Police Office on 101.