Cuba is the birthplace of the Mojito, although the exact origin of this classic cocktail is the subject of debate. One story traces the Mojito to a similar 19th century drink known as "El Draque", after Francis Drake. In 1586, after his successful raid at Cartagena de Indias Drake's ships sailed towards Havana but there was an epidemic of dysentery and scurvy on board. It was known that the local South American Indians had remedies for various tropical illnesses; so a small boarding party went ashore on Cuba and came back with ingredients for a medicine which was effective.

The ingredients were aguardiente de caña (a crude form of rum, translates as fire water from sugar cane) added with local tropical ingredients; lime, sugarcane juice and mint. Drinking lime juice in itself would have been a great help in staving off scurvy and dysentery. Tafia/Rum was used as soon as it became widely available to the British (ca. 1650). Mint, lime and sugar were also helpful in hiding the harsh taste of this spirit. While this drink was not called a Mojito at this time, it was still the original combination of these ingredients.

Some historians contend that African slaves who worked in the Cuban sugar cane fields during the 19th century were instrumental in the cocktail's origin. Guarapo, the sugar cane juice often used in Mojitos, was a popular drink amongst the slaves who helped coin the name of the sweet nectar.

There are several theories behind the origin of the name Mojito; one such theory holds that name relates to mojo, a Cuban seasoning made from lime and used to flavour dishes. Another theory is that the name Mojito is simply a derivative of mojadito (Spanish for "a little wet") or simply the diminutive of mojado ("wet"). Due to the vast influence of immigration from the Canary Islands, the term probably came from the mojo creole marinades adapted in Cuba using citrus vs traditional Isleno types.

The Mojito has routinely been presented as a favorite drink of author Ernest Hemingway. It has also often been said that Ernest Hemingway made the bar called La Bodeguita del Medio famous as he became one of its regulars and wrote "My mojito in La Bodeguita, My daiquiri in El Floridita." This expression in English can be read on the wall of the bar today, handwritten and signed in his name, although Hemingway biographers have expressed doubts about such patronage and about the author's taste for mojitos.