Ward was born in New York City to Colonel Samuel Ward, and his wife, Lucy. She was the granddaughter of Gideon Lee, a former mayor of New York City. At the age of three she accompanied her parents to Europe. She began to display a preference for the arts, and devoted herself by turns to the study of painting, sculpture, and music. By degrees, music absorbed her entirely, and her proficiency on the piano attracted attention.
On 10 November 1856, at age 19, she married Count Constantine de Guerbel. After a few years' stay in Europe, the family returned to New York, and soon afterward made the acquaintance of Henriette Sontag, who encouraged Ward to study singing. When the Ward family returned to Europe, Sontag gave Geneviève a letter of introduction to the composer Rossini. In 1862, after Ward's last role in La Traviata, she retired due to vocal difficulties. Ward later became a stage actress, noted for dramatic roles. Ward became a British subject late in life. It is not clear if this required her to renounce her citizenship in the United States.