Sheriff David Clarke says no hospital staff, patients or others were hurt.
Clarke said at a news conference that officers went to the 7th floor of the hospital in the Milwaukee suburb of Wauwatosa about noon Thursday after learning a man wanted for being a felon in possession of a firearm was visiting the neonatal unit.
Officers approached the man, who was holding a baby.
Clarke says the man put the baby down and ran, then produced a gun and turned around several times. The sheriff would not say whether the man fired any shots.
Officers shot and wounded the man, who is being treated at another hospital in the medical complex.