The victim has been named by media as Ester Pasqualoni, a 53-year-old cancer specialist and mother of two who died after being stabbed in the throat.
The attack took place in the car park of Sant'Omero hospital in Teramo, Abruzzo in central Italy as Pasqualoni was walking to her car at around 4pm on Wednesday.
One of Pasqualoni's colleagues, a medic at the hospital's emergency department, was the first to find her but was unable to save her life.
The suspect was reportedly found dead, apparently by suicide, in a nearby apartment on Thursday morning.
“We have an idea of who the killer may be and we are looking for him,” police had earlier told the Ansa news agency . “It is very probably a person who had been bothering the victim”.
Pasqualoni had made a complaint to police about a stalker, and a friend of the victim said in a Facebook tribute that they had discussed “that evil man who pursued you” many times.
Almost 3.5 million women in Italian have been victims of stalking, according to the most recent data from national statistics agency Istat, but only 22 percent of those report the act or seek help.
Italy has in recent years stepped up its efforts to tackle gendered violence. Changes pushed through in the past few years include the obligatory arrest of those caught in the act of stalking or physical abuse, and a law meaning that, once lodged, legal complaints cannot be withdrawn, and that victims must be kept up to date on their attacker's legal status.