Will Sweet told Australian radio station 3AW he was standing with his fiancee on a packed hill just off turn two at Albert Park during Sunday's race when the Danish Haas driver's car hit the track-side barrier sending his tyre and debris flying into the air.
"It slapped me in the arm and I was just standing there bleeding," he said.
"My arm was covering where my neck would’ve been, but if that had hit my fiancee, it would’ve got her right in the head.
"I realised how big it was and how heavy it was. Part of it was shredded and really sharp, if it hit me in a different angle, it could’ve been horrendous," he added.
Australian media published a picture of Sweet holding a large piece of debris with blood trickling down his forearm and another showing him having treatment from a medical official at the track.
Sweet said the area he was standing in was packed, with young children around, and that no race officials came to assist him.
"No one even came and looked," he said.
"My fiancee was pretty spooked by it and borderline shell-shocked."
Sweet added that the debris from Magnussen's car had flown "straight up, way over the fence" and into the crowd.
Australian Grand Prix Corporation (AGPC) boss Andrew Westacott said it looked like a "freak one-off" incident but that organisers would investigate.
"The debris fences are consistent around the world. We’re compliant with our FIA regulations," he told Australian media on Monday.
The AGPC is already under scrutiny after some fans invaded the track near the end of the race.
Late on Sunday, Formula One stewards ordered the AGPC to urgently produce a "remediation plan" in response to security and safety failures.
The AGPC allow fans to enter the track once the race is over for the podium celebrations, and Westacott said the AGPC had already started an investigation into how and why they did so beforehand.
"This was clearly a breach of what is a very robust protocol, a protocol that’s been developed and improved every year," he added.
Organisers said a crowd of 131,124 attended Albert Park on Sunday and a record total of 444,631 spectators across the race week.
