Spain captain Morata, 31, joined AC Milan in July after leaving Atletico Madrid.
The ex-Chelsea striker moved into a luxury home in Corbetta, a town of 18,000 people west of Milan.
But the former £60million Chelsea record buy felt his family's security was endangered after Corbetta's mayor Marco Ballarini posted news of their arrival on social media.
The report swiftly went viral among townsfolk, prompting the Moratas to move out.
Euro 2024 winner Morata fumed on Instagram as cited by Sports Central: "Dear Mr Mayor, thanks for violating my privacy. Thankfully I don't have anything of value. "The only treasures I have are my children, whose security has been jeopardised by you. "I thought that the town of Corbetta could afford me a certain amount of privacy. "Instead I find myself having to move house straight away, thanks to your inabilities to use social media and to safeguard your citizens."
Mayor Ballarini had previously proudly written: "Alvaro Morata is a Corbetta citizen. Here We Go! "The Spanish striker, newly signed by Milan, is finalising the paperwork for the move to his marvellous new home in our town. "I am a huge Inter Milan fan, but it is with pleasure that I offer Alvaro Morata a welcome to our big family in Corbetta."
Morata scored 24 goals in 72 Chelsea appearances following his 2017 arrival from Juventus.
However, he spent just 18 months at Stamford Bridge before returning home to join Atletico.
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