Isaiah Haastrup's parents had asked judges at the European Court of Human Rights (ECHR) in Strasbourg, France, to intervene after losing two legal battles in England.
An ECHR spokesman on Tuesday said three judges had examined issues and declared the couple's application "inadmissible".
A High Court judge gave doctors permission to provide only palliative care to 12-month-old Isaiah against the wishes of his parents, Lanre Haastrup and Takesha Thomas.
Mr Justice MacDonald analysed evidence at hearings in the Family Division of the High Court in January.
Specialists at King's College Hospital in London had said providing further intensive care treatment was futile and not in Isaiah's best interests.
Mr Haastrup and Miss Thomas, who are both in their 30s and from Peckham, south-east London, subsequently failed to persuade Court of Appeal judges to overturn Mr Justice MacDonald's decision.
They then made a written application to the ECHR.
"The court treated the case as an urgent matter," said the ECHR spokesman.
"In the light of all the material in its possession and in so far as the matters complained of were within its competence, the court found that they did not disclose any appearance of a violation of the rights and freedoms set out in the convention or its protocols."
His mother, Takesha Thomas told a private trial in January: "I am a Pentecostal Christian.
"For me, I don't think it is right to say who should live or who should die."
"If God wants to take the person, He will."
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