The body of the 35-year-old teacher, who worked in a school in Stabio near Mendrisio, was found on Sunday in woods in Italy, near the border with Switzerland at Gaggiolo.
She had wounds to the head and one fingertip.
In a statement on Wednesday, Ticino cantonal police said they had arrested a 42-year-old Swiss citizen for murder.
“It is the victim’s brother-in-law,” it said.
The arrest was the result of investigations in collaboration with the police and prosecutor of Como in Italy, police said.
According to Blick, the man has made a partial confession for the crime and is said to have dumped his sister-in-law’s body in the woods.
The primary school in Stabio where the victim worked released a statement saying it was “deeply affected” by the tragedy and was working with trauma experts to offer support to teachers and pupils.
Correction: An earlier version of this story stated that the arrested man was the victim's brother. This was incorrect - he was in fact the victim's brother-in-law. The story has been amended accordingly.