Prosecutors said the 19-month-old child fell to the ground during the struggle at Bloomfield Avenue on April 8.
Details emerged during a bail hearing for a 49-year-old Slovakian man accused of targeting the woman as part of an escalating feud.
Otto Dansco, of Templemore Avenue in the city, denies charges of common assault, threats to kill, possessing an offensive weapon in a public place, and criminal damage to a coat.
According to prosecution counsel Dansco grabbed the alleged victim - a vulnerable 20-year-old woman - while she was carrying her young daughter.
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It was claimed that he pointed a knife at the woman and said: “I will kill you.”
She was allegedly subjected to further verbal abuse, being called a “b****” and “prostitute”, the court was told.
The prosecuting barrister continued: “During the struggle the child of 19-months fell out of her arms onto the footpath and was later taken to the Royal Victoria Hospital for assessment to head injuries.”
Police are still seeking a medical report on the incident.
Mr Justice Burgess was told CCTV footage from the scene showed Dansco get something from the boot of a car and run up Bloomfield Road as if he was chasing someone.
The alleged victim was said to live in a different part of Belfast from the accused, who works for a cleaning services company.
Reference was made to other incidents potentially connected to the suspected feud. In some of those Dansco is the complainant.
Stressing that bail depended on imposing an exclusion zone around parts of the city, the judge said: “Listening to this the only way I can stop all of this is locking them all up.”
He also requested details on the addresses of all involved in a bid to keep them apart.
Dansco is set to be released on bail conditions that include having no contact with the alleged victim or members of her family.