Sarah Catt, 35 from Sherburn, North Yorkshire, deliberately brought on a miscarriage in the final stages of pregnancy, in what a judge described as "highly unusual circumstances".
It is understood she purchased a quantity of the drug Misoprostol, which can induce abortion, after researching and buying it on the internet.
Police believe she terminated her pregnancy within a week of its due date, but no trace of the baby's body has been found.
During the police investigation she persistently told officers she had undergone a legal termination.
But abortions in the UK can only legally be carried out up to 24 weeks and detectives said they had evidence Catt had been pregnant at her 30 week scan.
Appearing at Leeds Crown Court, Catt pleaded guilty to administering poison with intent to procure a miscarriage.
Detectives working on the case said Catt had not co-operated with the investigation and it was still unclear why she had taken such action.
Adjourning her sentencing hearing until September in order to allow time for psychiatric reports to be made, Mr Justice Maddison said: "There are highly unusual circumstances here."
Chief Inspector Kerrin Smith of North Yorkshire Police said: "Sarah Catt has today entered a guilty plea to the court. This marks the end of a long police investigation but many questions remain unanswered.
"In March 2010 Mrs Catt had confirmed pregnancy determined to be two days short of 30 weeks pregnant.
"Throughout this investigation she has claimed that this pregnancy was terminated legitimately even though that would not be legally possible.
"A legal termination can only be carried out up to 24 weeks in normal circumstances unless there are dire medical requirements to go beyond this. There were none in this case.
"During the investigation North Yorkshire Police gathered evidence that Sarah Catt purchased medication via the internet which could facilitate the labour and delivery of a child.
"The evidence shows this to have happened in the final stages of pregnancy, the third trimester, ie within the last week of the due date that this baby should have been born.
"Although she has entered a guilty plea today she has not co-operated with the investigation at any stage and so the question of what has happened to the baby that Catt was carrying remains unanswered. To date no remains of that pregnancy, nor body, nor child has been traced."
Catt was released on conditional bail to return to Leeds Crown Court on September 17.