Fiorentina condemned the "unacceptable and shameful" threats and offered their full support to all members of the club.
"Behaviour of this kind has no place in football or in any area of our society," the club said on their website.
"ACF Fiorentina, while thanking the many supporters who have already shown affection and support regarding these regrettable events, reiterates that there will never be any room for intimidation, hatred or violence."
Fiorentina next host Dynamo Kyiv in a Europa Conference League fixture on Thursday before welcoming Hellas Verona in Serie A on Sunday.