Those with anorexia proved to be poorer at empathising - like people with autism, who often have difficulty distinguishing people's different emotions - and scored more highly on tests of "systemising", an interest in pastimes with rules and patterns.
In a broader test, five times more of the anorexic girls got a score within the range typically associated with autism.
Researcher Simon Baron-Cohen, a leading expert on autism, said: "Traditionally anorexia has been viewed purely as an eating disorder.
"But this research is suggesting that underlying the surface behaviour, the mind of a person with anorexia may share a lot in common with the mind of a person with autism.
"In both conditions, there is a strong interest in systems.
"In girls with anorexia, they have latched onto a system that concerns body weight, shape and food intake."
Writing in the journal Molecular Autism, the researchers said it might be possible to help anorexics by shifting their focus away from foods to horse-riding, rowing or other pastimes that involve lots of rules and patterns.
Dr Tony Jaffa, who co-led the study, said: "Recognising that some patients with anorexia may also need help with social skills and communication and with adapting to change also gives us a new treatment angle."
- DAILY MAIL