We study the one-particle von Neumann entropy of a system of N hard-core anyons on a ring. The entropy is found to have a clear dependence on the anyonic parameter which characterizes the generalized fractional statistics described by the anyons. This confirms that the entanglement is a valuable quantity for investigating topological properties of quantum states. We derive the generalization to anyonic statistics of the Lenard formula for the one-particle density matrix of N hard-core bosons in the large N limit and extend our results by a numerical analysis of the entanglement entropy, providing additional insight into the problem under consideration.Facultad de Ciencias Exactas