The Mostar index of a connected graph is a well-known distance-based topological index. Hollow hexagons are coronoid systems that represent coronoid hydrocarbons belonging to the class of cycloarenes. They are formed by a single chain in a macro-cyclic arrangement consisting of linearly and angularly annelated hexagons, with exactly six angular hexagons. In this paper, we compute the Mostar index of hollow hexagons and find maximal and minimal values of the Mostar index over the set of hollow hexagons with a fixed number of hexagons.