The trial of Angela Hamilton, who is alleged to have disfigured Riggi for life, was postponed until next year, amid claims Riggi is not fit to give evidence in court.
Prosecutor Isobel Clark told Falkirk Sheriff Court that two doctors have confirmed Riggi is not fit to give evidence.
She asked for a further preliminary hearing to allow the Crown to get a report from the doctors concerned.
Defence agent Murray Aitken said he had not seen any medical reports and asked for his client's trial, originally set for later this month, to be adjourned. He said: "I haven't seen any reports, if they exist."
Sheriff Craig Caldwell agreed and adjourned the jury trial until January 13, extending the time-bar for the case until January 31.
Hamilton allegedly carried out the attack in Riggi's cell, at Cornton Vale Prison, near Stirling, on November 19, 2011.
Riggi, 49, originally from California, who is serving 16 years at the prison after admitting to stabbing her three children at their home in west Edinburgh, had to be rushed to hospital after the attack.
Hamilton, 40, currently a patient in a psychiatric ward at Leverndale Hospital in Glasgow, denies the attack.
Riggi killed eight-year-old twins Austin and Gianluca, and Cecilia, five, in August 2010, stabbing each eight times. She admitted culpable homicide on the grounds of diminished responsibility.