Pictures captured the moment people at the event scream and duck for cover as the fireworks appeared to blow up.
One woman who attended the show, at Stone SP Cricket Club, said her five-year-old son was hit on the chin by one of the stray fireworks.
About 3,000 people were said to have attended the display, with one capturing video of the screams of panic heard in the crowd.
The incident reportedly saw at least six people injured, including several other children.
After a brief pause to make an announcement requesting first aid, half the crowd walked out, with many of them in shock that the fireworks then resumed.
Witnesses described hearing people scream in terror as the firework exploded. “I saw something hit the floor and had this instinctive feeling something wasn’t going to go right,” one said.
"All you could hear was screaming after that. After it happened, everything froze. We didn’t know what was going on.
They added: "Half the crowd left. But then the fireworks started going off again. We thought ‘how can they continue with the display after what happened’ and we took the kids and left."
One woman said: "My son took some of a rogue firework to the chin. He’s five.
"He was terrified. Such a shame. Can’t fault the first aiders. I can’t believe they carried on either." Another said: "It was horrible, we left straight after that happened."
Stone Swynnerton Park Cricket Club and firework managers Monumental Fireworks refused to comment.
The ambulance service was contacted for comment. Staffordshire Police did not attend the event.
Thousands of firework displays will take place across the UK throughout the weekend to celebrate Bonfire Night.
Revellers were told to expect another washout across swathes of the country on Saturday as the remnants of Storm Ciaran bring more heavy rain.
Rain and wind will sweep northwards across England and Wales and those in the south can expect to see lightning.
By Sunday, those celebrating can expect conditions to be dry but cold with temperatures expected to dip.
In Scotland, firefighters warned about dangerous and unacceptable behaviour after being “bombarded” with fireworks, bricks and bottles in the week leading up to Bonfire Night.
Emergency crews who were mobilised to tackle a series of outdoor fires were targeted twice on Monday evening in Ardrossan, North Ayrshire.
Two further attacks took place in the Southhouse and Sighthill areas of Edinburgh on Tuesday, which was Halloween.