Wood rot fungi form one of the main classes of phytopathogenic fungus. The group includes many species, but has remained poorly studied. Many species belonging to the Ganoderma genus are well known for causing decay in a wide range of tree species around the world. Ganoderma boninense, causal agent of oil palm basal stem rot, is responsible for considerable yield losses in Southeast Asian oil palm plantations. In a large-scale sampling operation, 357 sporophores were collected from oil palm plantations spread over peninsular Malaysia and Sumatra and genotyped using 11 SSR markers. The genotyping of these samples made it possible to investigate the population structure and demographic history of G. boninense across the oldest known area of interaction between oil palm and G. boninense. Results show that G. boninense possesses a high degree of genetic diversity and no detectable genetic structure at the scale of Sumatra and peninsular Malaysia. The fact that few duplicate genotypes were found in several studies including this one supports the hypothesis of spore dispersal in the spread of G. boninense. Meanwhile, spatial autocorrelation analysis shows that G. boninense is able to disperse across both short and long distances. These results bring new insight into mechanisms by which G. boninense spreads in oil palm plantations. Finally, the use of approximate Bayesian computation (ABC) modelling indicates that G. boninense has undergone a demographic expansion in the past, probably before the oil palm was introduced into Southeast Asia.