ParknShop, which is controlled by Asia's richest man Li Ka-shing, apologised for selling cuts of a cheap and hard to digest fish, known simply as oil fish, as cod.
The supermarket chain said it had taken stocks of the fish off its shelves and was reviewing its labelling procedures.
"In particular we would like to apologise to those customers who may have suffered from digestive discomfort as a result of consuming this fish product," it said.
In the past couple of years, the supermarket has been found to have sold vegetables contaminated with banned pesticides, and fish from tanks that had traces of the cholera bacteria.
A government health spokeswoman said the 14 victims had complained of stomach aches after eating the fish, thought to have been sourced from mainland China.
Hong Kong has been plagued by health scares over produce imported from China, the former British colony's principle source of foodstuff.
Imports of many species of farmed fish, eels and eggs from mainland China were banned last year after cancer-causing chemicals were found in some samples.
There have been other recent scares over pork from China as well as poultry imports amid growing bird flu outbreaks in the region and elsewhere.
On Tuesday, environmental activists Greenpeace said tests it had carried out on fruit sold in open markets found high levels of contamination with banned pesticides including DDT.