Web footage showed the fire exploding when lit by a torch, sending crowds fleeing.
The event, a Lag baOmer celebration, saw hundreds of people gathered in Stamford Hill, when the bonfire suddenly exploded as it was being lit.
It is unclear what caused the blast, although there are reports fuel was poured on the fire.
London Ambulance Service and the Jewish volunteer ambulance service Hatzola attended at around 11pm.
Some 10 people were taken to the hospital with burns on their faces.
Police confirmed the injuries, adding: "No criminal allegations reported".
The festival of Lag B'Omer marks the anniversary of the death of Rabbi Shimon bar Yochai, a 2nd century AD sage.