During Monte Albán’s heyday, from 500 BCE to 800 CE, scholars believe the site was home to Zapotec (or Bènizàa) speakers. This attribution is based on studies of hieroglyphic texts from the site and general similarities to the Zapotec language spoken today. Following Monte Albán’s political collapse, however, other ethnic groups visited and used the site. Most notably, later groups reopened Classic Period tombs during the Late Postclassic (14-16th Centuries) to bury their dead. The most famous example is Tomb 7, which includes hundreds of offerings that are stylistically linked to Mixtec (or Ñuu Dzahui) people.
Information on Zapotec hieroglyphic writing from Monte Albán can be found here.
Information on Mixtec culture and language can be found here.