Siddiqui, who is accused of attempted murder of American soldiers in Afghanistan, disappeared mysteriously in Pakistan in 2003.
She is married to alleged terrorist Amar Al-Baluchi who is being held at Guantanamo Bay. She suddenly appeared in Kabul, apparently accompanied by her son.
She was examined and first diagnosed with psychosis on September 2 by the Bureau of Prisons psychologist Dr Diane McLean, according to a letter from the warden of Brooklyn's Metropolitan Detention Center to Judge Richard M. Berman.
Siddiqui "reported depressed mood, anxiety, ruminative thoughts concerning her son's welfare, poor sleep and moderate appetite".
The letter also describes a hallucination: "She also reported seeing her daughter in her cell, and was unable to apply appropriate reality testing to this phenomenon."
She politely declined to receive psychotropic drugs, the letter said.
Judge Berman ordered a physical examination of Siddiqui by a female doctor last week after a hearing which discussed, among other things, her refusal to meet her court-appointed lawyer Elizabeth M. Fink. She refused the physical examination on September 5.
On Monday, Judge Berman ordered a psychiatric examination.