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."