The schools in England and Scotland - six in Birmingham alone and two in Glasgow - received the threats this morning following which the buildings were evacuated.
Edgbaston High School for Girls in Birmingham, where 18-year-old Malala is enrolled, received a call just after 0800 GMT (1330 IST) making a bomb threat.
West Midlands Police is still investigating the call but pupils were allowed back into their classes after brief evacuation as the call is believed to be a hoax.
Today's calls follow similar calls last week which were also deemed as a hoax.
"This morning we have reports of a further six bomb threats, following similar threats made to several schools last week. At this stage there is nothing to suggest there is any credible threat to any of the schools," Detective Inspector Colin Mattison of West Midlands Police said in a statement.
"Our response officers have been sent to the locations to ensure there is no threat to anyone's safety and support the schools. A police investigation is ongoing to find the person responsible for these calls," he said.
A spokesperson for Police Scotlandsaid: "Two schools in Glasgow have received a threat via the telephone. Staff and police have searched both school buildings and nothing untoward was found.
"Schools are operating as normal and officers are continuing inquiries. At this stage, police are treating these incidents as malicious calls."
A number of schools and academies in and around Birmingham were also affected last Thursday.
A Russia-based Twitter group had claimed responsibility for threats last week, saying they intended to cause "mayhem".
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