'I'm next to you and can kill you'
Prof Hawking's daughter told police that threatening messages had begun flooding the scientist's social media profiles and one of his email accounts on Tuesday, Spanish News Today reported.
The woman, named Jenny Theresa C., had told the scientist she would kill him during the Starmus Festival, attended by Nobel laureates as well as musicians including Brian May, Brian Eno and Hans Zimmer, and famous astronauts.
She was arrested on Wednesday by police who found her in possession of a map showing Prof Hawking's itinerary while on the island.
After being detained, she told police that she was in love with the scientist and would never have hurt him.
Police said everything pointed to the woman being mentally unstable.
Jenny has been given a suspended four-month jail sentence in Spain. She has also been banned from approaching to within 500m of the scientist or communicating with him on social media for eight months.
The woman was arrested in a hotel in Tenerife, close to where Prof Hawking was attending a conference.
She had stalked him on social media before following him to the island.
"Women.They are a complete mystery"