Nasar Ahmed, 14, who had severe asthma and allergies, was reported ill last Thursday at Bow School in Tower Hamlets. He died on Monday afternoon.
A post-mortem examination will take place and the coroner has been informed. The Met said his death was being treated as unexplained.
Nasar was in supervised detention with three others in a ground-floor room.
His family told the BBC that he complained he felt ill and paramedics were called when it was discovered he did not have his inhaler or EpiPen.
Nasar's father, Ashrafu Zaman, arrived at the school before his son was taken to Royal London Hospital and said he thought he had already died.
He claimed Nasar would get disorientated so, when the school put him in detention, it did not acknowledge or take this into consideration.
The school, however, said there was a care plan in place which addressed Nasar's medical condition.
A statement from executive head teacher Cath Smith said: "I am very sad to confirm one of our Year 9 pupils, who was taken ill at school last Thursday, has passed away in hospital.
"The whole school community sends our thoughts and prayers to him, and to his family.
"We will continue to offer support to the family, his fellow pupils and teachers at this very difficult time.
"We will, of course, cooperate fully with investigations into the circumstances of this tragic incident and will also carry out a thorough review of what happened ourselves."
Social services have been informed.
The school's latest Ofsted report said it was judged to be "good and improving".
It said significantly more students were from minority ethnic backgrounds than in most schools, with the largest group of Bangladeshi origin.
More than three quarters of students were eligible for the pupil premium, additional funding to raise the attainment of disadvantaged students.
A schoolboy has died after he was taken ill during detention at an east London school.