Māhina Toki, who was from Great Barrier Island, was believed to be strapped into a harness on the deck and watching a movie, while her parents, Mark and Kiri were cooking dinner on Friday, a Fiji police spokesperson told Stuff.
When the parents returned to the deck, they could not find their daughter, and desperately began searching for her, the spokesperson said.
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The 13-month-old was found floating in the sea, and attempts to revive the young girl were unsuccessful.
Police said the family had been docked at Musket Cove since late July.
A Givealittle page for the family has been set up by Grace Palos' "fellow cruiser", with the Toki family appearing to be part of a group called Island Cruising New Zealand.
"Yesterday, tragedy struck and we lost beautiful Māhina, a 13-month-old who passed away in a fatal accident at Musket Cove," Palos wrote on the Givealittle.
"Māhina was tethered to her boat, Kalamari, yesterday afternoon when she worked free and found the water. By the time we could find her, it was too late."
According to the Facebook page Island Cruising New Zealand, an "incredible" team of medical professionals rushed to the young girl's side as she was brought into the dock.
"A paramedic, doctor, two nurses and a midwife as well as all the equipment, medication and oxygen that you would have in hospital," the post read.
"Sadly despite all of their best efforts, she did not make it. Please cuddle your little (and big) sailors tonight and help us carry little Māhina home with all the love of the worldwide cruising community."
Palos said Māhina was a "beautiful, happy, smiling child who loved the water and life on the boat".
"She had eyes that looked into your soul from the day she was born," Palos said.
Palos said Māhina's parents were in the process of "picking up their lives" and heading home to Great Barrier Island.
"The cruisers of Musket Cove are humbly asking for your assistance in raising funds for the family to help cover the cost of flights back home, funeral expenses and anything else Mark and Kiri need as they move forward," Palos wrote.
"To the beloved Mahina, may you forever live in peace, splashing with joy somewhere in the sea."
As of Sunday afternoon, donations to the Givealittle had hit $14,546 with a total of 138 people donating.
Fijian police said their investigation into the incident was ongoing.
