The incident occurred just after 11 p.m. when police officers on patrol heard two or three shots in the area of 553 Boylston Street in Copley Square.
They found the victim, identified as Ariel Lee, 22, of the South End, lying in the street with a gunshot wound to the chest.
Boston police Superintendent William Gross stated that they only have a vague description of the alleged suspect, a black male wearing a blue Hawaiian shirt who was seen fleeing down Boylston Street toward Clarendon Street.
Delaney Cooper, who identified herself as Lee's aunt, told the Boston Herald her nephew had just left Burger King when he was shot and is the father of two children.
Lee was taken to Boston Medical Center where he died from his wounds Friday morning.
No arrests have been made and police are asking anyone with information regarding the shooting to call the Boston Police TIPS line at 1 (800) 494-TIPS.
Homicide detectives are reviewing security video footage from area businesses and apartment complexes hoping to get a better description of the suspect.
Police also stated that they do not believe the shooting was random and Lee may have been targeted.