Marilyn Lemak, 41, seated in a wheelchair and dressed in a blue jail uniform, appeared expressionless during the hearing.
Her right forearm was heavily bandaged from what the authorities say was a suicide attempt, shortly after the killings, which took place last Thursday.
Judge Steve Culliton approved a request by Mrs Lemak's lawyer for a psychiatric examination, on the understanding that it will not determine whether she is fit to stand trial on murder charges.
The killings have horrified neighbours in Naperville, a suburb of Chicago. They say that the Lemak family, comprising a father who was a doctor, a mother who was a registered nurse and three children ages seven, six and three, was picture perfect.
However, David Lemak, an emergency room physician, allegedly told his father that Mrs Lemak had been in and out of a deep depression since the birth of their last child.
Mrs Lemak is accused of drugging the children, putting them to bed and then suffocating them by placing her hand over the mouth and nose of each child.
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