A man has died after falling from an eighth-floor balcony at an apartment complex in Sydney's east.

Emergency services were called to a unit block on Onslow Avenue in Elizabeth Bay just before 8 a.m. on Sunday. Police had attended the building as part of ongoing inquiries and were attempting to speak with a 40-year-old man believed to be inside one of the units.

Officers spoke with a 38-year-old woman inside the apartment, who refused entry. She later left the unit while police remained outside. Shortly after, police were alerted that a man had fallen from a balcony.

Officers found the 40-year-old man and provided first aid until paramedics arrived. NSW Ambulance crews treated the man for critical injuries, but he died at the scene.

Police have since cordoned off the area while investigators work to piece together the events leading up to the man's death and any interaction police had with him before the fall. Detectives from another command have been brought in to lead the investigation. This investigation is standard procedure when a death occurs in connection with a police operation. The case will also be reviewed by the NSW Police Professional Standards Command and monitored by the Law Enforcement Conduct Commission.

Police have not yet released the man's identity and are urging anyone with information to contact them.