London Fire Brigade (LFB) said 15 fire engines were sent to the building on Craven Walk, Hackney, after the alarm was raised shortly before midnight on Tuesday.
Crews faced hazardous conditions after flames severely damaged the basement and ground floor of the three and four-storey building, thought to be a Jewish faith school.
Station manager Nicola Lown said: “The ground floor has partially collapsed into the basement leading to hazardous conditions.
“Two fire rescue units are also on the scene and their equipment is being used to shore up the ground floor.
“This will enable crews wearing breathing apparatus to gain better access to the fire in the basement.”
LFB said the cause of the fire is not known at this stage and there were no reports of injuries.