The impact of the mud and rocks forced the building's walls and roof to cave in while guests were inside dancing.
Twenty-nine people were injured and had to be pulled from the debris following the incident on Sunday in the Andean city of Abancay, officials said.
Local media report that the incident occurred during heavy rain in the area.
About 100 guests were present at the Alhambra hotel at the time of the incident, the head of Peru's National Civil Defence Institute (Indeci), Jorge Chávez, told local media.
Some 50 people were believed to have been close to one of the walls that collapsed, he added.
Images posted on social media by Indeci showed rescuers searching through the rubble and carrying people on stretchers.
#LluviasIntensas ocasionan colapso de pared en Hotel Alhambra mientras se celebraba un matrimonio en Tamburco, Abancay - Apurimac.@bomberosPE y @PoliciaPeru continúan con trabajos de búsqueda de personas.
— INDECI (@indeciperu) January 27, 2019
Hasta el momento se reportan:
13 fallecidos.
30 heridos.#COENmonitorea pic.twitter.com/IFzCuthsq5
The mayor of Abancay, Guido Chahuaylla, said that every effort was made to ensure that rescuers were able to reach those trapped in the rubble. The wounded were taken to a local hospital, he added.
Local media report that the Alhambra hotel is situated close to a steep slope, and the wall that collapsed into the building was built to protect it from mud and rocks.
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