Storni was born in Sala Capriasca, Switzerland to an Argentine beer industrialist living in Switzerland for a few years. There, Storni learned to speak Italian. Following the failure of the family business, they opened a tavern in the city of Rosario, Argentina, where Storni worked at a variety of chores.
In 1907, she joined a traveling theatre company which took her around the country. With them she performed in Henrik Ibsen's Spectres, Benito Pérez Galdós's La loca de la casa, and Florencio Sánchez's Los muertos.
Back in Rosario she finished her studies as a rural primary teacher, and also started working for Mundo Rosarino and Monos y Monadas local magazines, as well as Mundo Argentino.
In 1911 she moved to Buenos Aires, seeking the anonymity of a big city. The following year her son Alejandro was born, the illegitimate child of a journalist in Coronda.
In spite of her economic difficulties, she published La inquietud del rosal in 1916, and later started writing for Caras y Caretas magazine while working as a cashier in a shop.
Storni soon became acquainted with other writers such as José Enrique Rodó and Amando Ruiz de Nervo , and established friendships with José Ingenieros and Manuel Ugarte.
Her economic situation improved, which allowed her to travel to Montevideo, Uruguay. There she met the poet Juana de Ibarbourou, as well as Horacio Quiroga, with whom she would become great friends. Her 1920 book Languidez received the first Municipal Poetry Prize and the second National Literature Prize.
She taught literature at the Escuela Normal de Lenguas Vivas, and she published Ocre. Her style now showed more realism than before, and a strongly feminist theme. Solitude and marginality began to affect her health, and worsening emotional problems forced her to leave her job as teacher.
Trips to Europe changed her writing by helping her to lose her former models, and reach a more dramatic lyricism, loaded with an erotic vehemence unknown in those days, and new feminist thoughts in Mundo de siete pozos (1934) and Mascarilla y trébol (1938).
A year and a half after her friend Quiroga committed suicide in 1937, and haunted by solitude and breast cancer, Storni sent her last poem, Voy a dormir ("I'm going to sleep") to La Nación newspaper in October 1938. Around 1:00 AM on Tuesday the 25th, Alfonsina left her room and headed towards the sea at La Perla beach in Mar del Plata, Argentina. Later that morning two workers found her body washed up on the beach. Although her biographers hold that she jumped into the water from a breakwater, popular legend is that she slowly walked out to sea until she drowned.
Her death inspired Ariel Ramírez and Félix Luna to compose the song Alfonsina y el Mar ("Alfonsina and the sea"), which has been performed by Mercedes Sosa, Tania Libertad, Nana Mouskouri, Mocedades, Andrés Calamaro, Katia Cardenal and many others.
Also, fifty years after her death, she inspired the Latin American artist Aquino to incorporate her image into many of his paintings.
Storni once referred to men as el enemigo, "the enemy." Much of Storni's work focuses on what she sees as the repression of women by men. This often takes the form of personal insults directed at men in general.