A 'Family Fun Day' at Cockatoo Island on Sunday ended with patrons shoving and screaming at each other as they waited to get off the island, with ferries unable to cope with the numbers.
The event was jointly organised by the Australian National Maritime Museum and Sydney Harbour Federation Trust.
People attending the Family Fun Day said that some ferries were full upon arrival at the wharf, and families were fighting each other to get on the ferries that were able to take passengers.
Jessica McIntosh took her 14-month-old son to the event and said the scenes at Cockatoo Island on Sunday were frightening.
"It was absolutely packed. There were so many people," she said. "There were a lot of people right on the edge of the wharf, including children and people with babies in their arms.
"People weren't getting on the ferries, they were shoving and fighting to get on. Two ladies were screaming at each other."
Ms McIntosh said crowds were not being controlled even when staff did arrive to assist.
"It took 20 minutes to get staff down there. There were some ferry staff but it took a long time for them to organise," she said.
She said that she only got on a ferry after being assisted by a crew member who had to fight crowds to help her get on.
"I kept getting pushed away when I tried to get on. I was quite stressed. A crew member told me he'd help me get on and he helped me get on a ferry.
"I was there for an hour and it was still packed when I left."
She said that the situation had been frightening and that it was lucky no one was injured.
"It was incredibly dangerous. People could have easily fallen into the water. It shouldn't have ever happened," she said.
A spokesperson for the Australian National Maritime Museum said large crowd numbers and poor weather conditions had led to the overcrowding.
"Approximately 2500 people attended over the course of the day, which was an increase on the attendance numbers of previous years," they said.
"The rain shower which hit at 3pm did cause a number of visitors to head to the ferry wharf at the same time. Unfortunately the ferry services at the time couldn't take many passengers as they were already full before reaching Cockatoo Island, with other passengers also heading home.
"Sydney Harbour Federation Trust liaised with Sydney Ferries throughout the afternoon and additional services were put in place to help accommodate the additional demand."
A Transport for NSW spokesperson said: "Harbour City Ferries, the operators of Sydney Ferries, provided three additional Cockatoo Island services yesterday in response to customer demand.
"Other services with capacity were requested to stop at Cockatoo Island to also assist with demand."
Families heading to the fun day were encouraged to travel by ferry to Cockatoo Island which is accessible only by water.
The incident comes a week after Transport NSW announced major changes to Sydney's ferry routes which will see Cockatoo Island receive its own ferry service in late November.