This work applies Matrix Completion (MC) – a class of machine-learning methods commonly used in the context of recommendation systems – to analyze economic complexity. MC is applied to reconstruct the Revealed Comparative Advantage (RCA) matrix, whose elements express the relative advantage of countries in given classes of products, as evidenced by yearly trade flows. A high-accuracy binary classifier is derived from the MC application, with the aim of discriminating between elements of the RCA matrix that are, respectively, higher/lower than one. We introduce a novel Matrix cOmpletion iNdex of Economic complexitY (MONEY) based on MC, and related to the degree of predictability of the RCA entries of different countries (the lower the predictability, the higher the complexity). Differently from previously-developed economic complexity indices, MONEY takes into account several singular vectors of the matrix reconstructed by MC, whereas other indices are based only on one/two eigenvectors of a suitable symmetric matrix, derived from the RCA matrix. Finally, MC is compared with a state-of-the-art economic complexity index (GENEPY), showing that the false positive rate per country of a binary classifier constructed starting from the average entry-wise output of MC is a proxy of GENEPY.