The reduced-rank regression (RRR) model allows for the possibility that the matrix of regressor parameters is rank deficient. Most approaches used for estimating the RRR model require the assumption that the predictors’ covariance matrix is non-singular. This is a known issue when dealing with small sample size data, but it is also relevant for data with a compositional structure, vectors carrying relative information. A possible way to circumvent the non-singularity assumption is to perform sparse RRR. A recent strategy suggests obtaining sparsification by imposing cardinality constraints. This procedure is argued to be more efficient, moreover it does not rely on tuning penalty terms. In this work, we propose the implementation of a cardinality constraint sparse RRR for compositional data and test its feasibility on a data example available in the literature.