Members of the Picornaviridae are important and often zoonotic viruses responsible for a variety of human and animal diseases. However, the evolution and spatial dissemination of different picornaviruses circulating in domestic animals are not well studied. We examined the rate of evolution and time of origin of porcine enterovirus G (EV-G) and porcine kobuvirus species C lineages (PKV-C) circulating in pig farms in Vietnam and from other countries. We further explored the spatiotemporal spread of EV-G and PKV-C in Southwest Vietnam using phylogeographic models. Multiple types of EV-G are co-circulating in Vietnam. The two dominant EV-G types among isolates from Vietnam (G1 and G6) showed strong phylogenetic clustering. Three clades of PKV-C (PKV-C1-3) represent more recent introductions into Vietnam; PKV-C2 is closely related to PKV-C from Southwest China, indicating possible cross-border dissemination. In addition, high virus lineage migration rates were estimated within four districts in Dong Thap province in Vietnam for both EV-G types (G1, G6) and all PKV-C (C1-3) clades. We found that Chau Thanh district is a primary source of both EV-G and PKV-C clades, consistent with extensive pig trading in and out of the district. Understanding the evolution and spatial dissemination of endemic picornaviruses in pigs may inform future strategies for the surveillance and control of picornaviruses.