The Marine Conservation Society said it had removed mackerel, an oily fish packed with omega 3, from its latest version of its "fish to eat" list, and it should be eaten only occasionally.
The warning comes after the Marine Stewardship Council, which certifies fish stocks that are managed sustainably, suspended its certification of the north east Atlantic mackerel fishery.
Atlantic populations of mackerel have moved north west into Icelandic and Faroe Islands waters, prompting their fishermen to fish more stock than was previously agreed and causing a dispute between the countries that target the fishery.
Bernadette Clarke, fisheries officer at the Marine Conservation Society (MCS), said: "The stock has moved into Icelandic and Faroese waters, probably following their prey of small fish, crustaceans and squid.
"As a result, both countries have begun to fish more mackerel than was previously agreed.
"The total catch is now far in excess of what has been scientifically recommended and previously agreed upon by all participating countries.
"Negotiations to introduce new catch allowances have so far failed to reach agreement."
The conservation group said good alternatives to mackerel were herring and sardine, and if people wanted to continue to buy mackerel, they should ensure it is as sustainable as possible - for example, fish caught locally using traditional methods.
Another fish taken off the "fish to eat" list is gurnard, because of a lack of data on population levels and concerns about how stocks of the increasingly popular fish are being managed.
Because the fish has been historically caught accidentally as "bycatch" by fishing vessels targeting other species, there are no catch restrictions - but if stocks are being increasingly targeted, they need to be managed sustainably, the MCS said.
Many gurnard which are caught are discarded, a wasteful practice which sees usable fish thrown back into the sea, because there is still relatively low demand for them, Ms Clarke added.
But the latest version of the "fish to eat" list shows that herring stocks, coley and Dover sole from the English Channel are all good to eat with a clear conscience.
Whiting from the Celtic Sea also appears on the list for the first time.
Cod stocks from the North Sea are still below recommended levels, the MCS said, but a number of other popular wild fish are given the green light to appear on the dinner plate, including haddock and lemon sole.
And farmed species are on the list, including organic Arctic charr, sturgeon caviar from closed fish farming systems, mussels, tiger prawns, Atlantic halibut and salmon and rainbow trout.
Ms Clarke said: "As world population, fish consumption and reliance on fish imports from outside the European Union increases, the importance of knowing what we are eating, as well as where and how it is caught, is essential to allow consumers to make the most sustainable choice for the future of our fish."
A spokesman for Defra said: "The continued sustainability of mackerel is vitally important and is increasingly threatened by the actions of the Faroe Islands and Iceland.
"We are extremely concerned that an agreement on fishing rights has not yet been reached.
"That is why the UK continues to seek a new agreement that is fair to all."
Ian Gatt, chief executive of the the Scottish Pelagic Fishermen's Association, said the MCS reacted far too quickly in taking mackerel off the "fish to eat" list.
He said: "Mackerel is still being sustainably caught and it is important that the consumer is made aware of this.
"The north east Atlantic stock is in robust health and the sustainable fishing practices of our fleets have actually led to an increase in abundance in the stock in recent years.
"However, the over-fishing of the stock by Iceland and the Faroes is leading to some uncertainty over the future, and this is why it is essential that these countries come back to the negotiating table and agree a sensible deal."
He said scientific advice showed the mackerel stock was above the safe biological minimum, and at current exploitation rates would not fall below that level until next year.
The advice said catches must be reduced, and the EU and Norway have recognised that and are reducing quotas by at least 15% this year, he said.
Paul Williams, chief executive of seafood industry body Seafish, said: "It is important to recognise that science and the fishing industry are in agreement on this one - stocks of mackerel are plentiful.
"What we are all looking at though is the future of the stock and the cautionary advice now being received from some certification bodies if the dispute about the north Atlantic quota remains unresolved.
"The UK industry and supply chain is fully switched on to the issue and has a good recent track record of working with environmental organisations to provide the best advice to consumers.
"That advice as it stands is that we can continue eating mackerel, albeit it with a greater awareness of the issues surrounding it, and due political process will find a solution in time to quotas."
Scottish Labour's rural affairs spokeswoman Claire Baker MSP said: "Scottish mackerel brings in millions to the Scottish economy each year and this decision will potentially impact on UK sales as consumer confidence may drop.
"Today's news is not out of the blue and the Government must take some responsibility and engage with consumers and retailers to ensure confidence in Scottish mackerel remains high."
Tavish Scott, fisheries spokesman for the Scottish Liberal Democrats, said the EU should impose sanctions on the Faroe Isles and Iceland before their illegal fishing of mackerel hits Scotland's industry even harder.
Mr Scott said: "The illegal catching of mackerel, the failure of the EU to impose sanctions and the withdrawal of an important status for sustainable caught fish will lead to harder financial times for the industry.
"The Scottish and UK governments have worked hard to force sanctions in the absence of international agreement over the right mackerel quota.
"They must redouble their actions in the face of the EU's apparent cave-in."
The Shetland MSP said Lerwick-based fish processors Shetland Catch had seen its turnover fall from £71 million in 2010/11 to £48 million a year later, "purely as a result of the mackerel market collapsing through oversupply of fish being caught by Faroe and Iceland".