The ability of relatives of the 11-month-old girl to protect her from harm was being assessed by Cheshire East Council's social workers.
Mr Justice MacDonald, sitting in Liverpool, said the assessments contained "patent defects".
The council said it had not met the "high professional standards" expected.
The private family court hearing was considering where the girl should live after she suffered serious head injuries while living with her parents.
A previous court judgement found she had sustained head injuries on two separate occasions that were "on the balance of probabilities" caused by her mother.
The court also found the girl's father had caused her emotional harm.
The council had chosen some relatives to care for the baby but other family members had objected.
None of the family members involved can be named for legal reasons.
The judge said assessments contained "patent defects" caused by social work which was "at best lackadaisical and at worst in contravention of statutory guidance".
He named two social workers who he said had carried out "inadequate and fundamentally flawed" assessments, adding that "the serious mistakes made by Cheshire East Borough Council in this case are of very real concern and must not be repeated".
Kath O'Dwyer, responsible for children's services at the local authority, said: "Cheshire East Council apologises unreservedly for the failings highlighted in the court judgement.
"Lessons will be learned and staff training and procedures will be reviewed and reinforced to ensure such failings are not repeated".
Further assessments of the relatives' ability to care for the child have been ordered by the judge, with the costs to be met by Cheshire East Council.
A council has apologised after a High Court judge labelled its social workers "lackadaisical" for the way they dealt with the case of a vulnerable baby.