She had been suffering from depression and sought medical help and attended a therapy after her divorce from Portuguese journalist Jorge Arantes in the early 1990s, the author told the newspaper.
"Mid-twenties life circumstances were poor and I really plummeted," Rowling said, adding: "The thing that made me go for help ... was probably my daughter."
"She was something that earthed me, grounded me, and I thought, this isn't right, this can't be right, she cannot grow up with me in this state," she continued.
Rowling added: "We're talking suicidal thoughts here, we're not talking `I'm a little bit miserable'."
The author, praised for remotivating an entire generation of children to read with her seven-part story on boy wizard Harry Potter, wrote the first book as a single mother living in poverty in Edinburgh.
She later became one of the world's richest women, with a personal wealth of more than $NZ1.285 billion.