In that year, a muleteer traveling from Veracruz to Guatemala noticed that there was an extra mule in his pack. As he passed in front of the San Sebastián hermitage, the mule fell to the ground under the weight of the load. Even when the load was removed and they tried to get the mule to stand up, it rose briefly and then died instantly. When the load was inspected, they found an image of the Virgin Mary accompanied by a Christ and a sign that said "The Virgin at the Foot of the Cross." In light of these events, the bishop at the time, Bartolomé Bohorquez, ordered the construction of a sanctuary honoring the Virgin.

Construction began in 1682, led by chaplain Don Fernando Méndez. The building was completed in 1689, and in 1697, the convent was finished and the temple was consecrated to the Virgin of La Soledad, the patroness of the town of Oaxaca.

It has a magnificent yellow quarry stone façade in the form of a folding screen with a clear baroque style. It is considered one of the most beautiful in Oaxaca and is richly adorned with several niches containing statues of St. Nicholas of Bari, St. Marcial, St. Sebastian, St. John the Apostle, St. Joachim, St. Augustine, St. Peter, St. Paul, St. Rose of Lima, St. Catherine of Alexandria, St. Nicholas of Tolentino, St. Anne, St. Lucia, Archangel Gabriel, St. Stephen, and in the center, the Virgin of La Soledad.

The atrium courtyard has two entrances, one to the south and another to the east. The latter connects with Plaza de la Danza and the Socrates Garden, famous for its delicious ice creams.

Inside, the statue of the Virgin of La Soledad, a beautiful organ, and 18th-century paintings on the sides of the presbytery stand out. The image of the Virgin of La Soledad can be seen on the main altar.

At the back of the Basilica, there is the Religious Museum where the history of the temple's foundation is narrated, and some religious artifacts are exhibited. Although small, it is worth a visit.

The former convent currently serves as offices for the municipality of Oaxaca.