On Thursday evening the girl from Sehnde near Hanover tried to pull the firework out of her top but was unable to free herself before it went off, badly burning her.
Police are now investigating her 14-year-old friend for dangerous bodily harm.
Every New Year police and hospitals warn of the dangers of fireworks and firecrackers, which are an integral part of the German New Year celebrations.
The Association of Fireworks Industries (VPI) estimates that Germans blow €133 million worth of fireworks into the air every Silvester.
Police stress particularly that fireworks smuggled in from eastern Europe can be dangerous and should not be bought on the black market, as they can detonate sooner than expected.
A hospital in western Germany this year published a photo of a hand maimed by a firecracker which exploded before the person could throw it.
The shocking image unsettled many social media users and was quickly deleted.
But fire services have also published a photograph of a replica hand burnt by a firework to publicize the dangers of the explosives.
On Friday police officers stopped a car carrying 1,200 illegal fireworks as it tried to cross into Germany from the Czech Republic.
German customs say that they seized 1.85 tonnes of illegal firecrackers at Germany’s borders in 2015.