Financial markets are paradigmatic examples of complex systems and have been compared to ecological networks in which different species (firms) interact and co-evolve. A central object governing species dynamics in ecology is the community matrix, whose elements are closely related to pairwise interspecific interaction coefficients. Using this ecological analogy we propose a method, based on the Maximum Entropy (MaxEnt) principle, that allows us to infer candidates for an economic community matrix from time series data of market values. To assess the usefulness of this picture, we construct community matrices for a set of companies belonging to the Fortune 500 list and perform a community analysis on the resultant networks. This analysis shows these networks to strongly reflect the known industry groupings of the firms. We conclude therefore that our community matrices capture non-trivial information about the interaction of firms, not immediately apparent from the covariance of market values. We anticipate our approach being useful in elucidating further aspects of market structure, as well as forming the basis of forecasting market dynamics.