Researchers modelled the impact of rising temperatures on more than 600 species between 2001 and 2050.
Warmer waters could decrease ocean oxygen levels and significantly reduce fish body weight.
The scientists argue that failure to control greenhouse gas emissions will have a greater impact on marine ecosystems than previously thought.
Previous research has suggested that changing ocean temperatures would impact both the distribution and the reproductive abilities of many species of fish. This new work suggests that fish size would also be heavily impacted.
The researchers built a model to see how fish would react to lower levels of oxygen in the water. They used data from one of the higher emissions scenarios developed by the Intergovernmental Panel on Climate Change (IPCC).
Although this data projects relatively small changes in temperatures at the bottom of the oceans, the resulting impacts on fish body size are "unexpectedly large" according to the paper.
As ocean temperatures increase, so do the body temperatures of fish. But, according to lead author, Dr William Cheung, from the University of British Columbia, the level of oxygen in the water is key.
"Rising temperatures directly increase the metabolic rate of the fish's body function," he told BBC News.
"This leads to an increase in oxygen demand for normal body activities. So the fish will run out of oxygen for growth at a smaller body size."
The research team also used its model to predict fish movements as a result of warming waters. The group believes that most fish populations will move towards the Earth's poles at a rate of up to 36km per decade.
"So in, say, the North Sea," says Dr Cheung, "one would expect to see more smaller-body fish from tropical waters in the future."
Taking both the movements and the physiological impacts of rising temperatures together, the research team concludes that fish body size will shrink between 14% and 24%, with the largest decreases in the Indian and Atlantic oceans.
When compared with actual observations of fish sizes, the model seems to underestimate what's actually happening in the seas.
The researchers looked at two case studies involving North Atlantic cod and haddock. They found that recorded data on these fish showed greater decreases in body size than the models had predicted.
Other scientists say the impact could be widely felt.
Dr Alan Baudron, from the University of Aberdeen, UK, has studied changes in the growth of haddock in the North Sea. He says this latest research is a "strong result".
He believes it could have negative implications for the yields of fisheries. And it could also seriously impact the ability of fish to reproduce, he adds.
"Smaller individuals produce fewer and smaller eggs which could affect the reproductive potential of fish stocks and could potentially reduce their resilience to other factors such as fishing pressure and pollution," he told BBC News.
The authors point out a number of limiting factors in their study, including uncertainties in the predictions for the climate and the oceans. According to Dr Cheung, further research is required.
"Our study shows that climate change can lead to a substantial decrease in the maximum body weight of fish. We need to look more closely at the biological response in the future."
The research has been published in the Journal Nature Climate Change.
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