Numerous networked systems feature a structure of nontrivial communities, which often correspond to their functional modules. Such communities have been detected in real-world biological, social and technological systems, as well as in synthetic models thereof. While much effort has been devoted to developing methods for community detection in traditional networks, the study of community structure in networks with higher-order interactions is still not as extensively explored. In this article, we introduce a formalism for the hypermodularity of higher-order networks that allows us to use spectral methods to detect community structures in hypergraphs. We apply this approach to synthetic random networks as well as to real-world data, showing that it produces results that reflect the nature and the dynamics of the interactions modelled, thereby constituting a valuable tool for the extraction of hidden information from complex higher-order data sets.