Pams owner Foodstuffs said it was taking the matter "very seriously" as it did with all cases of foreign matter in products.
Spokeswoman Antoinette Laird said discussions with the supplier and visual inspection of the images provided led Foodstuffs to conclude the foreign matter was most likely fish skin and bone.
She said Pams fish fingers were made from natural fish fillets, not minced fish product, so there was a "very small risk" other fish material could be in the finished product.
The company said its fish fingers had a statement on the product label, telling consumers bones were possibly present.
"But following this incident we are discussing what manufacturing changes could be made to further reduce the chance of fish bones or skin ending up in the finished product," Mrs Laird said.
She said the fish fingers supplier had a risk management plan in place and the company was not aware of any similar issues with the product.
Ms Torrey said a Foodstuffs employee picked up the fish finger and the foreign object yesterday to take them away for testing.