A US team of researchers found that forecasted shifts in climate by 2070 would occur too quickly for species of grass to adapt to the new conditions.
The species facing an uncertain future include wheat, corn, rice and sorghum, which provide almost half of the calories consumed by humans.
The findings appear in the Royal Society Biology Letter journal.
Not only does the grass family (Poaceae) of more than 11,000 species form the staple of people's diets across the globe, natural grasslands cover about a quarter of the planet's land area and provide a home to a rich diversity of dependent flora and fauna.
The team from the University of Arizona, US, observed: "Thus, if climate change has strong negative impacts on grasses, there might be significant consequences for both global biodiversity and for humans."
In order to gain an insight into the impact of projected climate change on the world's grasses, they estimated the rates of climate change niche change in a representative sample of 236 grass species and compared these rates with rates of projected climate change by 2070.
"A climatic niche is basically the temperature and precipitation conditions where a species occurs," explained co-author John Wiens from the university's Department of Ecology and Evolutionary Biology.
"What is important about it is that if you are thinking about one species living in one place and it can only survive under a limited set of conditions then, as the climate changes, it either has to shift its climatic niche or it is going to go locally extinct."
He told BBC News: "In other words, it either has to accommodate those new conditions or it will not be able to survive there any more."
The team examined how quickly the grass species' climatic niches were able to change, based on they had changed in the past.
"What we found was that they do not change all that much - a few degrees Celsius over a million years. There are just small changes over long time scales," Dr Wiens observed.
"In some ways, that is the most important part of the story; these climatic niches generally seem to change relatively little and relatively slowly.
"Then we looked at future climate projections for a range of localities, and we asked how much they were going to change."
The team found that the difference between the rates of change in the study's grass species' climate niche and projected changes in a location's climate was often "20,000-fold".
"The findings are similar across all the groups so they could be applied to wild species as well as to the cultivated ones. There is no way that cultivated species are somehow exempt from our findings," Dr Wiens added.
These finding present a bleak outlook; apparently squashing the hope that crop species would be able to cope with a warming world.
The study does not show species going globally extinct, rather it highlights how conditions are projected to change in a way that is beyond the climate niche of species, therefore species are likely to disappear from that location.
But this does have implications for farmers growing food crops.
"For people living in parts of the world that perhaps do not have the [technology], such as in the developing world where crop production is much more dependent on climate, it doesn't matter if the species go extinct because it will grow elsewhere.
"What does matter is that if your crops go extinct or decline."
While the study did not look at the issue of food security, Dr Wiens said there was a lot of promising research underway in the form of identifying opportunities to develop "climate-proof" food crops for future generations.
"What has been shown, though, is that people continue with business-as-usual, there will be serious problems."
"One of the things that would help us alleviate this problem is wild relatives because we know that the species we have domesticated have a reduced genetic variation. That genetic variation, found in the wild relatives, is exactly what you want to allow them to adapt to different conditions."
But Dr Wiens as highlighted: "We can look to our food crops' wild relatives, but the problem is they are going to be highly endangered by climate change as well."
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A study has highlighted the risk posed by projected climate change on the world's ability to grow enough food.