The judges said the consent of the father was not required if the mother did not wish to disclose his identity.
Monday's ruling overturned earlier court orders which said a woman needed the father's consent if she wanted to be a legal guardian of her child.
Women's rights activists have welcomed the ruling and called it "progressive".
The case was filed by a Delhi mother who had asked the court's permission to become her child's "legal guardian" without informing the father who, she said, did not know about the child's existence.
A trial court and the Delhi high court had earlier ruled that she needed to disclose the father's name and get his consent for the purpose.
But on Monday, Justices Vikramjit Sen and Abhay Manohar Sapre said there was "no need to insist on the father's name" and that in the case of an unwed mother, her "name is sufficient".
The judgement has been praised by lawyers and activists:
India's Supreme Court has in a landmark ruling said an unwed mother does not have to reveal the name of her child's father to claim guardianship.