Experts admitted surprise at the findings because so many other studies have linked red meat to physical health risks.
The team made the link after a study of 1000 Australian women.
Professor Felice Jacka, who led the research by Deakin University, Victoria, said: "We had originally thought that red meat might not be good for mental health but it turns out that it actually may be quite important.
"When we looked at women consuming less than the recommended amount of red meat in our study, we found that they were twice as likely to have a diagnosed depressive or anxiety disorder as those consuming the recommended amount.
"Even when we took into account the overall healthiness of the women's diets, as well as other factors such as their socioeconomic status, physical activity levels, smoking, weight and age, the relationship between low red meat intake and mental health remained.