Zaheer Ahmed from Rotherham said his nephew was jumping on a bouncy castle in an indoor playground at Gulliver's Valley Park when he landed on metal railings placed close to the inflatables.
The 38-year-old said her sister, Sonya Ahmed, 33, brought her son to the park with her friends and their children to celebrate her youngest child's fourth birthday.
He said: "The children had a full day playing with the rides and there was no issue.
"As they were asked to exit the area because there was a time limit, he couldn't stop himself from bouncing off and landing straight to the railings.
"She then straight away picked him up and shook him up to the side of the bouncy castle because he looked like he fainted as his eyes were shut."
He said her sister then brought the boy home when she noticed that his left arm was swelling and decided to send him to Rotherham General Hospital for further check up.
This was when she was told that her son suffered a serious fracture and needed immediate surgery to keep the bones intact.
The mum-of-three said: "The barrier should not have been there. It's a bad break on his arm and it's really disappointing.
"We need to see how he’s healing. We were also told he might have problems with his arm when he’s older”
Zaheer said since the incident, his nephew's anxiety has "gone through the roof" as he became overly careful with any movements he's about to make.
He said a day after the incident he went back to the park to take some pictures of the area where the incident happened for photographic evidence.
However, to his shock, he managed to enter the park without any identification, a ticket, or a child.
"I've gone in without any ticket, no identification, nothing. If I had no identity, nobody knows who I am. If I caused some damage, you can't trace me.
"They also said they have no CCTV in there - what would happen if I were to kidnap a child? There was no wristband or a stamp either."
He said the park has since replaced the metal railings and replaced them with wooden barriers within a safer distance.
In response, a spokesperson for Gulliver’s Valley, said: “As a family business we take the health and wellbeing of our customers extremely seriously and we are conducting our own internal investigations into these reports.
"Any action that is found to be required in order to improve the health and safety aspects of our park will of course be undertaken immediately.
“We have built a strong reputation for safeguarding over the last 43 years. It is important to note that both of these incidents were reported retrospectively and we are now in contact with Mr Ahmed to address his concerns with him directly.”
Zaheer said the park's health and safety director has on Tuesday apologised to the family personally on the park's behalf and that they are looking into these incidents seriously.
He also said he has reported the incidents to the council and the police.