Mr Justice Holman heard evidence from a psychiatrist involved in the woman’s treatment, a lawyer representing her husband and her mother at a Court of Protection hearing in London.
According to the BBC, the court heard the woman began asking for a termination after she is believed to have stopped taking her medication.
She is thought to have made the decision to protect the health of her baby and announced she wanted to have a termination last month, the Independent reports.
Lawyers representing the health authority told the judge that the woman had a ''chronic and severe mental disorder''.
''She is pregnant and she has requested a termination of her pregnancy,'' they said in a written statement.
“She is believed to lack the capacity to make a decision regarding the termination of her pregnancy due to her mental disorder.''
They said the health authority was asking the judge to decide whether a termination of her pregnancy is in her best interests.
Mr Justice Holman was told that the woman suffers bipolar disorder - a condition formerly known as manic depression - and had said she would probably kill herself if she was forced to give birth and "locked up".
Her solicitor also reported her saying she would kill the baby if she was forced to carry it to term.
The psychiatrist said he was "100% certain" that the woman lacked the capacity to make a decision about termination.
A lawyer representing her husband, who was at today's hearing, said he agreed with the psychiatrist's evaluation, and the woman's mother told the judge: "I know my daughter when she is well and she is definitely not well."
The hearing began on Monday and the Mr Justice Holman will hear further evidence on Tuesday, with a decision expected in the next few days.
Mr Justice Holman ruled that neither the woman nor the health authority responsible for her care should be identified. He also said the unit where she was being treated should not be identified.
The Court of Protection is part of the High Court and analyses issues involving sick and vulnerable people.