The interactions between plants and arbuscular mycorrhizal fungi (AMF) maintain a crucial link between macroscopic organisms and the soil microbial world. These interactions are of extreme importance for the diversity of plant communities and ecosystem functioning. Despite this importance, only recently has the structure of plant-AMF interaction networks been studied. These recent studies, which used genetic data, suggest that these networks are highly structured, very similar to plant-animal mutualistic networks. However, the assembly process of plant- AMF communities is still largely unknown, and an important feature of plant-AMF interactions has not been incorporated: they occur at an extremely localized scale. Studying plant-AMF networks in a spatial context seems therefore a crucial step. This paper studies a plant-AMF spatial co-occurrence network using novel methodology based on information theory and a unique set of spatially explicit species-level data. We apply three null models of which only one accounts for spatial effects. We find that the data show substantial departures from null expectations for the two non-spatial null models. However, for the null model considering spatial effects, there are few significant co-occurrences compared with the other two null models. Thus, plant-AMF spatial co-occurrences seem to be mostly explained by stochasticity, with a small role for other factors related to plant-AMF specialization. Furthermore, we find that the network is not significantly nested or modular. We conclude that this plant-AMF spatial co-occurrence network lacks substantial structure and, therefore, plants and AMF species do not track each other over space. Thus, random encounters seem more important in the first step of the assembly of plant-AMF communities.