The focus of the inquiry surrounds a two-door car in the grounds of the hospital in south Belfast.
Crime scene investigators have erected a forensic tent over the vehicle.
Police have also closed off nearby Dunluce Avenue as the investigation continues.
A PSNI spokeswoman said: “Police are currently at the scene of an ongoing incident in the Lisburn Road, Belfast.
“There are no further details at this stage.”
Belfast City Hospital remains open as the scene continues to be examined.