Or maybe what was the first book to be published that was written by a woman?
Interestingly enough, the first novel or "Psychologically complex" novel was written by a woman 1000 years ago in Japan. And!, it holds up very well to modern audiences. I read it in college and was absolutely riveted. It didn't fell like it had come from so long in the past. It's Not like reading an epic tale at all. A very tragic hero is at the centre of it.
Women were the primary writers in Heian culture, and noble women's reputations were often a function of their prowess in writing. Think of the court as an endless Comp-Lit graduate dormitory.
The simple-minded answer would be the Gospel of Mary, an apocryphal book -- that is to say, an early Christian writing that is not accepted as canonical. As, most unusually, the Gospel of Mary is known from three separate, independent, surviving fragments in two different languages, there is no doubt that it was an important and widely-distributed scripture of the early Christian church.
The question is, of course, who actually wrote it, and when. Most scholars place it at about 150CE, although a leading authority on early Christian writings, Karen L King, the Hollis Professor of Divinity at Harvard, thinks it was written in the time of Christ. Although a biblical Mary is obviously rejected as being the author, it is likely that a writing which places a woman front and centre at this era did have a woman involved in its creation. But Karen King's careful wording is "The first book written in the name of a woman".
A translation, and related discussion: The Gospel of Mary of Magdala : Jesus and the first woman apostle, Karen L King, Polebridge Press, 2003
There is so much on the web about Mary Magdalene that is at the fruitcake end of the spectrum that Wikipedia counts as one of the better sources for a quick overview of the "gospel" and the story of its modern discovery.