Northumbria Police said Kayll was attacked at an address in Linton, Northumberland, on Sunday evening along with a 15-year-old boy, and died in hospital days later.
The force said a 49-year-old man was detained in Glasgow on Friday.
Kayll, 47, worked as a teacher at Atkinson House school, which caters for children with social, emotional and mental health issues.
In a statement, the school in Seghill, Cramlington, said: “Our school community is saddened to hear the news of Caroline’s passing.
“Our thoughts and prayers are with her family at this very difficult time.”
The teenage boy suffered serious, but non-life threatening injuries and was discharged from hospital.
A 58-year-old man, arrested earlier this week on suspicion of assisting an offender, has since been released under investigation, police added.