Mr Justice Hayden made the decision after hospital bosses said the child could die or suffer a stroke if she was not treated urgently.
The girl’s parents said their religious beliefs would not allow them to consent to a transfusion, but did not object to the judge making the order.
Leeds Teaching Hospitals NHS Trust, which has responsibility for the girl’s care, made the application in the Family Division of the High Court in London on Wednesday.
A specialist told Mr Justice Hayden the child was suffering from sickle cell disease, an inherited blood disorder, and her condition had deteriorated. He said he feared a “life-threatening event” if the girl was not given a blood transfusion soon.
The girl’s father broke down as he told the judge that he wanted his daughter to live but could not agree to a transfusion.
After analysing evidence at a public hearing, Mr Justice Hayden said the law allowed judges to make such rulings.
The girl, who cannot be identified, is being treated at Leeds Children’s Hospital.
Jehovah’s Witnesses say the Old and New Testaments of the Bible “clearly command us to abstain from blood”.
“God views blood as representing life,” the religion’s website says. “So we avoid taking blood not only in obedience to God but also out of respect for him as the giver of life.”
Earlier, at a separate hearing in the Family Division, another judge approved an agreement between hospital bosses and a teenage Jehovah’s Witness who refused to be treated with blood products or given a blood transfusion.
Mr Justice Moor had been due to oversee a trial after hospital bosses asked him to decide what would be in the boy’s best interests.
But he was told doctors had taken the view that the boy should not be treated with blood products against his wishes and were trying a different approach.
The court heard the teenager was born abroad and had lived in England with a relative for some time. His father is dead and his mother’s whereabouts are unknown.
Mr Justice Moor, who approved the agreement at a private hearing, said neither the boy nor the NHS hospital trust involved could be identified in media reports.
That case echoes the plot of Ian McEwan’s 2014 novel The Children Act, which was made into a film starring Emma Thompson.
In the novel, a judge decides a 17-year-old Jehovah’s Witness should have a blood transfusion against his wishes, to save his life.
Additional reporting by Press Association
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