The attack took place in broad daylight outside the Henry Dunant Hospital in the 16th district of Paris.
Police union official Rocco Contento told BFM TV there had been an argument between the gunman and the woman. The shootings happened after a man tried to intervene.
According to France Télévisions, the woman, in her thirties, was a security agent at the hospital. She is being treated in intensive care.
The male victim, who died from his wounds, has not yet been identified.
Shocked witnesses said the hooded assailant escaped on a motorbike after firing off several rounds.
Police have cordoned off the area and are actively searching for the assailant.
"It is not a terrorist attack, it was probably a case of score-settling," Francis Szpiner, mayor of the 16th arrondissement, told reporters.
An investigation is now under way for murder and attempted murder.
