The 44-year-old nurse died from a gunshot wound to the head in May this year.
A police investigation over the past few months discovered that the girl had been reproached by her mother for performing badly at school, Corriere reported.
As a way of stopping her daughter from spending too much time on social networks, the mother is said to have taken away her laptop and computer.
Police said that this was the motive behind the alleged murder. The teenager was arrested on Thursday in the town of Melito Porto Salvo, in Reggio Calabria.