Police believe the distraught mother of Katerina Laktionova put her remains into the suitcase after she died from her condition, Italian media say.
The body was found, wrapped in a black plastic bag, by fishermen on 25 March.
Gulnara Laktionova confessed to a friend, Italian media said.
Police found no evidence of violent death during an autopsy.
The Corriere Romagna newspaper reported that a male friend became concerned that he had not heard from the mother and daughter since 10 March, and then learned about the grisly discovery.
He phoned the young woman's mother several times, and she eventually told him she had shut the body in the suitcase and thrown it into the water, after keeping it in her house for at least a week, the newspaper said.
Gulnara Laktionova, 48, flew back to Russia shortly before the body was found, reports say.
She told her lawyers that she had "lost her mind" and that "the world fell apart," according to the Italian news agency ANSA.
Katerina Laktionova had been hospitalised for a short period in Italy in 2015 and had requested a residency permit in February to continue treatment for her anorexia, ANSA said.
Gulnara Laktionova was quoted by Russia's NTV as saying: "I don't know anything. I don't remember anything. I'm not feeling quite right in the head."
The Italian investigation is continuing.
Previous reports had linked the body to a missing Dublin-based woman, who has not been seen since 10 February when she boarded a ship to Genoa.
Chinese-born Xing Lei Li is still unaccounted for, and her husband Daniel Belling was arrested in Rome attempting to board a flight to Dublin last month.
An emaciated female body found in a suitcase floating near the Italian port of Rimini has been identified as a Russian woman who had been suffering from anorexia.