That means they are rated threatened, endangered or vulnerable by the International Union for Conservation of Nature, the global scientific authority on extinction risk.
The researchers, headed by Trisha Atwood, an ecologist at Utah State University, assessed data about 22,166 species. Overall, there are more predator species and more at-risk predators in total, but a larger share of plant-eaters are in strife.
University of Miami biologist Mauro Galetti said the study "changes our biased idea that conservation projects should focus mostly on top predators".
Galetti said large herbivores were crucial, especially in forests.
"A world without herbivores would be a disaster for any natural ecosystem."
Atwood told AP that threats such as other species, climate change and habitat loss hit herbivores harder, and size was possibly part of the reason. Herbivores such as rhinos were often bigger and needed to eat more. They required more land and yet their habitats were shrinking, she said.
Other animals can range further which helps them survive.
Atwood concluded: "We need to think about herbivores as being kind of the poster child of extinction."
In terms of getting people to care about conservation, in a fractured world where too much demands our attention, predators have a definite advantage.
A brightly coloured tiger has an outsized glamorous appeal of strength, power, danger and beauty, while retaining some of the cat-appeal of a mini-me tiger sleeping on the sofa.
Sea turtles are a quieter, harder sell. But all species deserve as much protection as we can muster.
And a key lesson from the pandemic is that wild animals generally, and their habitats, need to be looked after and preserved, for their sake and for ours.
Nature has a way of biting us back if we don't show respect.
