Tower Hamlets Council in east London said the story was inaccurate and the Independent Press Standards Organisation (Ipso) upheld its complaint.
The Times trailed the ruling on its front page and published it in full on page two.
In a series of articles about the case, the newspaper alleged that the Christian girl's foster carers stopped her eating bacon, confused her by speaking Arabic and took away her crucifix necklace.
Tower Hamlets complained about the third article, published on 30th August 2017, which said the child was "removed from her Muslim foster parents yesterday and reunited with her family as a judge urged councils to seek 'culturally matched placements' for vulnerable children".
The council said it had "actively sought" to place the child with her grandmother, who was from a Muslim background.
In its ruling, the watchdog said: "Ipso's complaints committee found that the article gave the impression that the judge had found that the placement was a 'failure' by the council; and that this was why she was 'removing' the child from her current foster carers, and placing the child with the grandmother.
"The committee ruled that this was a distortion. The complainant had been in the process of assessing the grandmother, and, when those assessments were complete, it applied to the court for the child to be placed with her.
"The complainant had in fact agreed at the hearing that the child should live with the grandmother."
It said the newspaper had failed to take care not to publish distorted information.
Ian Brunskill, assistant editor of the Times, told a Commons committee on Tuesday that the story had caused "enormous offence" and upset.
Tower Hamlets Council chief executive Will Tuckley said the authority had been "impressed by the care and commitment of the foster carers".
He added: "We felt it was important to make the complaint to defend our foster carers and protect children in foster care, along with standing up for our diverse communities.
"We always said that, although cultural and religious matches are very important in foster care cases, there are other important factors to consider such as the child being close to their school and blood relatives.
"Ultimately, we have to make the best decision taking into account the foster carers that are available in an emergency situation. What matters most is that we place the child is in a loving and supportive home.
"From the start we had significant concerns about the validity of the allegations about the foster carers; for example, one allegation was that they did not speak English, even though that is a prerequisite for any foster carers."
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