Officers were called to a report of concern for the teenager around 1.20pm. He was taken by ambulance to hospital, but died a short time later.
A post mortem examination has confirmed that Hamdan died from natural causes.
As with any sudden death, a report has been sent to the Procurator Fiscal.
Chief Inspector Jocelyn O'Connor said:
"This has been a tragic incident which has deeply affected everyone at the school. Our thoughts remain with Hamdan's family and friends at this very difficult time and we are providing our support to them.
"They have requested privacy and I would ask their wishes are respected."
Hamdan's family have released the following statement through their solicitor Aamer Anwar:
"Our family is left devastated by the sudden and tragic loss of our beautiful boy Hamdan who brought so much joy to our lives.
"We want to assure Hamdan's friends and our community that this was an entirely natural death and could not have been predicted.
"A full police investigation is being carried out, but we can confirm that Hamdan had a pre-existing heart condition that had never been detected, and sadly his death could have occurred at any time.
"There is no one to blame for his loss, it was God's will.
"We know that Hamdan's loss is being deeply felt by his friends and teachers and we would urge those who have engaged in rumours on social media to stop, it is untruthful and compounding our grief.
"Please take down the posts, the running commentary is unhelpful to the children, teachers and our family who have been left deeply traumatised and devastated.
"We know that Hamdan's teachers and friends did everything possible to save his life and for that our family will for ever be grateful to them."
Andrew Sharkey, Headteacher of St Kentigern's Academy, said:
"Hamdan was an exemplary student and he will be hugely missed by the St Kentigern's community.
"Hamdan was a bright and diligent young man, and conscientious in his studies. He was very friendly, popular with his classmates and he had a close group of friends. He was always polite and well-mannered in class and popular with his teachers. Hamdan was kind and thoughtful in all he did and he was always happy, with a beautiful smile.
"Our thoughts and prayers remain with his family and friends at this incredibly difficult time.
"Our dedicated team at St Kentigern's Academy will continue to provide support to pupils and we would ask that the family's privacy is respected."