According to New Zealand Food Safety, histamine poisoning happens when the fish is not chilled adequately. If this happens in certain fish, including trevally, it can be toxic to humans.
People who eat the infected fish are likely to experience a number of undesirable symptoms including tingling and burning around the mouth, facial flushing, diarrhoea, skin rash, nausea, abdominal cramps, vomiting, dizziness, palpitations, headaches and possibly respiratory distress.
Symptoms can last for up to 12 hours but there are no long-term effects.
The company has apologised to customers for the "inconvenience".
"We sincerely apologise for any inconvenience caused and will be providing a refund of the cost of the ingredient. We want to assure you the safety and quality of our ingredients is our highest priority."
The meals are delivered nationwide to homes on Sundays.
An Auckland resident who ordered a Hello Fresh box this week said he and his family were concerned after eating the trevally.
"I understand the most common cause of this is due to inadequate refrigeration or spoiled fish.
"Hello Fresh needs to provide more information on its website as to how this occurred and provide assurance about the safety of its ingredients."
The company provides a phone number if people have already eaten the food and are concerned.
Hello Fresh said it was informed by a seafood supplier that a batch of trevally customers had received potentially showed elevated histamine levels.
"HelloFresh has immediately contacted all potentially affected customers directly advising them to dispose of the white fish delivered this week," said a company spokesperson.
"While only a batch of the fish was affected, the supplier has issued a recall on this week's white fish to ensure customer safety."
The company said it was now working closely with the supplier to investigate the cause of the issue, and had paused the supply until the full investigation was finished.
The number of people affected by the supplier issue was low but Hello Fresh "sincerely" apologised for the impact the recall had had on customers.
New Zealand Food Safety's Food Compliance national manager Melinda Sando said Hello Fresh had not made contact with the government organisation before starting their recall.
Food businesses were able to take the initiative and conduct a recall on their own where they assessed a potential risk to consumers, but they were required to notify food safety officials within 24 hours.
"We are contacting Hello Fresh to understand how the issue arose and whether the fish has been supplied to other businesses," said Sando.
If anyone had fallen ill from eating the fish, they were encouraged to seek medical attention and contact their local district health board public health unit, she said.