Anna E. Munch is growing up in a cultural family; a gathering place for art, music and literature, Her father, the writer Andreas Munch, is Norwegian and related to Edvard Munch, while her sister, Helga, later becomes a photographer. Munch herself has a distinct artistic talent, and as a child she is drawing portraits. She trains as a painter, studying in Paris with the renowned history painter Jean Paul Laurens and later in Denmark with Julius Paulsen. She makes her debut at the Charlottenborg Spring Exhibition in 1898.

Anna E. Munch remains unmarried and childless and dedicats herself instead to her art, which is primarily possible due to the family's wealth. She shares a large part of her life with the writer Sofie Breum and also has a close and lifelong friendship with the sculptor Niels Hansen Jacobsen.