The woman was feeding her child while observing a matter in the Victorian County Court on Thursday when the judge addressed her directly.
"Madam you will not be permitted to breastfeed a baby in court," he said.
"It will be a distraction and I'll have to ask you to leave."
She then got up and left the courtroom with her child.
Melbourne obstetrician Nisha Khot said the incident was appalling.
"We've tried so hard to get past so many barriers for women who want to breastfeed and to have this happen in a court of law is just not acceptable at all," Dr Khot told AAP.
"Babies have been breastfed in the parliament of this country and in other parliaments.
"I don't think there is any public space in which breastfeeding a baby should be unacceptable."
She said breastfeeding had long-term implications for mother and child so anything stopping that could impact their health.
People are not allowed to eat, drink or wear clothing such as sunglasses and hats in court.
Pregnant and breastfeeding women are protected by anti-discrimination laws in areas of public life including work, schools, universities, shops or rental properties.
However, the Victorian Equal Opportunity and Human Rights Commission's website does not state whether the legislation applies to court rooms.
The Parenthood chief executive Georgie Dent said it was incredibly humiliating to be asked to leave somewhere because of breastfeeding.
"It creates this impression of some sort of shame around feeding your baby," Ms Dent said.
"If we police people for that we just increase the isolation that mothers experience and we create a situation where breastfeeding becomes that much more difficult."
Judges are immune from civil liability on the basis of promoting independence.
The County Court declined to comment.
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