Officers confirmed that the suspected shooter, who was armed with a rifle and a handgun, was also dead.
Police arrived at the scene on Wednesday afternoon at St Francis Hospital in three minutes - which they say ensured the death toll wasn't higher.
Multiple injuries had also been confirmed, officials added.
Speaking at a press conference on Wednesday, Deputy Police Chief Eric Dalgleish said: "Right now we have four civilians that are dead, and one shooter that is dead."
