Eleven of the injured were children, who suffered mainly minor burns and shock, said police.
The blast, involving 90kgs of fireworks, happened as around 350 people watched a free display in Willenhall, in the West Midlands on Thursday night.
The injured were taken to hospitals in Wolverhampton and Walsall. The most seriously hurt was a child, with burns to a hand and arm, Walsall police said.
The display had been organised by Hooty's Discount Superstore as a promotional night for customers. Managing director Richard Beaumont, 43, said it was the fourth display his store had organised and was going normally until near the end.
"Suddenly the whole thing exploded. Fireworks, which were supposed to be going upwards, were spiralling out in all directions like a giant spider.
"At first the crowd thought it was some kind of mega firework, but it didn't take them long to realise that this was not the case."
Mr Beaumont said the fireworks shot across the car park and over the road after displays were knocked over by the force of the original blast.
He said that staff helped the injured before paramedics arrived at the scene. "People were screaming `Get out, get out'. It was all absolute chaos."
Mr Beaumont, who said he would not be holding another display, said a specialist firework display company had been hired for the event.
Fire investigators examined the scene in a bid to establish exactly how the accident happened.
The director of the National Campaign for Firework Safety, Noel Tobin said: "We have been campaigning for years to have proper training and licensing introduced into this country.
"It is good news that no-one was seriously injured in the accident but all too often people are badly hurt or killed."