The Investigative Committee said suspect Gyulchekhra Bobokulova, a 38-year-old native of Muslim-majority Uzbekistan, would undergo psychiatric and drug tests to determine "her mental condition."
The maximum punishment for the murder of a minor is life in prison although women offenders cannot be sentenced to more than 25 years in jail in Russia.
A defendant cannot be sentenced to jail term if found to be legally insane.
"The investigation is currently taking exhaustive measures to study the personality of the accused and establish the motives of the crime she committed," the Investigative Committee said in a statement.
In a court on Wednesday, the 38-year-old told journalists that "Allah ordered" the killing.
Video footage that emerged on the Internet appeared to show the mother-of-three saying the attack was "revenge" for President Vladimir Putin's bombing campaign in Syria, which began in September.
The Investigative Committee swiftly said she had "long been diagnosed with schizophrenia", while the Kremlin called her a "deranged person."
Some have suggested that the Uzbek nanny might have been radicalised by Muslim hardliners.
One of Bobokulova's sons, Rakhmatillo Ashurov, was questioned by Uzbek police and said his mother had become very devout after meeting Dzhurakulov, the newspaper said.
Bobokulova's son reportedly also said his mother wanted to take him to the Islamic State in Syria where she could "freely wear an Islamic veil and live according to Sharia law" and where he could "join jihad."
The son said he had told his mother he wanted to move to the United States or South Korea and had no plans to travel to the Islamic State, the newspaper said.