The man, from Leeds, told a family court judge that he made a “false allegation” because he was angry with the woman.
Mr Justice Cobb said NSPCC officials alerted local authority social services staff in Rotherham and an investigation began.
The woman, a teacher, denied shaking the girl but said her husband abused her. She also said her husband “suffers from his stupidity”.
A note written in Ukrainian found on the mantelpiece of their home read: “1: Do not react to shouting”, “2: Remain calm despite everything”, “3: Appeal to God when (my husband) rise up against me”, “4: Pray for (my daughter) and to God so that He will protect and defend me.”
The woman told Mr Justice Cobb that she had the note “available as a reference point” to help her “cope with the abuse”.
The details emerged in a ruling by Mr Justice Cobb following a hearing in the Family Division of the High Court in London.
Social workers had asked for decisions to be taken about the girl’s future - and the judge said he had made preliminary rulings after analysing evidence and legal argument at a hearing earlier this month.
Mr Justice Cobb said the family could not be identified but the man came from Leeds and the woman from Kharkiv, north-east Ukraine.
He said bosses at Rotherham Metropolitan Borough Council had launched family court litigation.
The judge said: “The father telephoned the NSPCC and reported that the mother had shaken (the girl) ‘like a rag doll’ on more than one occasion.
“The NSPCC made a child protection referral to the local authority, who undertook a joint investigation.”
He added: “The father has now almost completely retracted the allegation, and maintains that no incident occurred involving shaking of (the girl). The father says that he was motivated to make a false allegation by anger towards the mother.”
Mr Justice Cobb said the pair married in the Ukraine three years ago after meeting via an internet dating site and started living in England in late 2015.
He said the woman had written to a friend in the Ukraine earlier this year and said: “At home (my husband) is a real tyrant, immoral tyrant at that. He suffers from his stupidity.”