The Qinghai-Tibetan Plateau offers one of the most extreme environments for yaks (Bos grunniens). Although the genetic adaptability of yak and rumen metagenomes is increasingly understood, the relative contribution of host genetics and maternal symbiotic microbes throughout early intestinal microbial successions in yaks remains elusive. In this study, we assessed the intestinal microbiota succession of co-inhabiting yak and cattle (Bos taurus) calves at different weeks after birth as well as the modes of transmission of maternal symbiotic microbes (i.e., rumen fluid, feces, oral cavity, and breast skin) to their calves’ intestinal microbiota colonization. We found that the fecal microbiota of yak and cattle calves after birth was dominated by members of the families Ruminococcaceae, Bacteroidaceae, and Lachnospiraceae. The Source Tracker model revealed that maternal fecal microbes played an important role (the average contribution was about 80%) in the intestinal microbial colonization of yak and cattle calves at different weeks after birth. Unlike cattle calves, there was no significant difference in the fecal microbiota composition of yak calves between 5 and 9 weeks after birth (Wilcoxon test, P > 0.05), indicating that yak may adapt to its natural extreme environment to stabilize its intestinal microbiota composition. Additionally, our results also find that the intestinal microbial composition of yak and cattle calves, with age, gradually tend to become similar, and the differences between species gradually decrease. The findings of this study are vital for developing strategies to manipulate the intestinal microbiota in grazing yaks and cattle for better growth and performance on the Qinghai-Tibetan Plateau.