Languages are transmitted through channels created by kinship systems. Given sufficient time, these kinship channels can change the genetic and linguistic structure of populations. In traditional societies of eastern Indonesia, finely resolved cophylogenies of languages and genes reveal persistent movements between stable speech communities facilitated by kinship rules. When multiple languages are present in a region and post-marital residence rules encourage sustained directional movement between speech communities, then languages should be channeled along uniparental lines. We find strong evidence for this pattern in 982 individuals from 25 villages on two adjacent islands, where different kinship rules have been followed. Core groups of close relatives have stayed together for generations, while remaining in contact with, and marrying into, surrounding groups. Over time, these kinship systems shaped their gene and language phylogenies: Consistently following a postmarital residence rule turned social communities into speech communities.