The first precedent of the current Museum of Menorca is the Municipal Museum of Mahón, which was inaugurated on 4th November 1889, in the old building of the Principal de Guardia, opposite the Town Hall itself. Its promoter was Joan Seguí Rodríguez and its initial collection was made up of donations from private individuals. The first pieces, fragments of Roman tombs found in Mahón, were donated by Pere Monjo Monjo, the centre's curator.

After the death of the Museum's founder in 1890, the Town Council offered the conservation of the collection to the teaching staff of the Institute. Francesc Hernández Sanz, a teacher at the Institute and curator of the Museum since 1898, was in charge of consolidating the collection.

In 1906, the collection passed to the Museum of the Ateneo de Mahón, until 1944, when it was integrated into the recently founded Provincial Museum of Fine Arts, organised by Félix Merino and María Luisa Serra Belabre. The Town Council of Mahón donated the palace of Can Mercadal, headquarters of the Casa de Cultura and today a public library, where the new Museum was located in November 1948. In addition to the assets contributed by the Ateneo de Mahón, those of the Commissariat of Excavations, the Sub-Commission of Monuments and others from private collections were also added, so that the collection was considerably increased.

From 1953 to 1967, under the direction of María Luisa Serra, the Museum's collection was increased with the acquisition of works of art and donations from Menorcan painters, and an important documentation and dissemination work was carried out. During this period, the Museum also housed archaeological material from the important excavations that were being carried out on the island, such as the Naveta des Tudons, the Naveta de Rafal Rubí, the Talatí de Dalt settlement, the Basílica des Fornàs de Torelló and the Basílica de la Isla del Rey, among others.

In 1975, under the name of the Museum of Menorca, it became part of the network of the Patronato Nacional de Museos (National Museum Board). But the building threatened ruin, so it was closed to the public. Five years later, in 1980, a property belonging to the Mahón Town Council, the former Franciscan convent, was donated to the State as the Museum's definitive headquarters, and work began on refurbishing the building.

In 1984, management was transferred to the Balearic Government. And in 1986, part of the refurbished building began to function. The restoration of the cloister of San Francisco provided the Museum with new items: ceramics from the 12th and 18th centuries and polychrome tiles from the 18th and 19th centuries.

The temporary rooms were opened to the public in 1995 and three years later, the permanent rooms were opened, inaugurating the new headquarters of the Museum of Menorca.

The Museum's collection has grown thanks to the numerous archaeological excavation projects carried out by Menorcan archaeologists and others linked to the University of the Balearic Islands, the University of Boston and the University of Sassari. The pieces that the British archaeologist Margaret Murray had found in the 1930s during her excavations in Trepucó and in the Talayotic settlement of Sa Torreta and which were in Cambridge were also recovered.

The donations and deposits of ethnological, artistic and industrial material that began in the 1990s and during the first decade of the 21st century, both from private individuals and from various entities, have also been essential to complete the collection.

From 2007 to the present day, a team of archaeologists from the Museum has been carrying out excavation and restoration work at Cornia Nou, a Talayotic settlement located near Mahón.

The Consejo Insular de Menorca (Island Council of Menorca) has been managing the Museum since September 2011. The institution offers a digitised collection where part of the collection can be consulted.

The current headquarters of the Museum of Menorca is the former Franciscan convent of Jesús, which was part of the Church of San Francisco, located next door. Its origins date back to the 15th century, but there are no architectural remains from this period, since as a result of a Turkish attack on the city, the building was destroyed in 1535.

The building that has come down to us was built between the 17th and 18th centuries, with alterations at the beginning of the 19th century.

On the ground floor of the convent were the porter's lodge, the chapter house, the kitchen, the pantry, the cellar, the refectory and the grammar and philosophy schools. The friars' cells and other rooms were located on the upper floors.

The Franciscans had to leave the convent in 1835, with the ecclesiastical confiscation of Juan Álvarez Mendizábal. The building was taken over by the municipality and, before becoming the Museum's headquarters, it was occupied by various entities that put it to different educational and cultural uses: it was the Casa de la Misericordia, the Nautical School, the Public Library and the Secondary School.

The Museum building is organised on three floors that surround the Baroque cloister with a square floor plan, with low arches and a wing that juts out in the southern area. It combines the superimposition of classical orders with Baroque elements. The temporary exhibition rooms and the assembly hall occupy the ground floor, around the cloister, and the permanent exhibitions are located on the first and first floors.