The toddler died on Christmas Day and its body was discovered by a search party comprising police, family and residents of Bethany, located about two kilometres from eSwatini's industrial town, Matsapha.
The baby was taken by its father after he had quarrelled with its mother on the evening of December 25, 2019.
It is believed that the 22-year-old father is responsible for hanging the child on a school fence surrounding Bethany Mission Primary School.
Chief Police Information and Communications Officer, Superintendent Phindile Vilakati said when the body of the baby girl was found it was hanging with a wire on the side of the fence that was next to a bush.
"The police are still searching for the father as he seemed to have disappeared without trace" she said.
The toddler's distraught grandmother Sibongile Ndwandwe said: "I had never met the baby until when his parents arrived on Christmas Eve. I learnt that they picked an argument on Christmas Day, which led to my son taking the baby away with him."
The missing man's mother said her son left a note in his room where he bade her farewell and also extended an apology to her.
The police said according to their records, the child was the youngest to die by hanging in the kingdom.