Precise fabrication of molecular assemblies on a solid surface has long been of central interest in surface science. Their perfectly oriented growth only along a desired in-plane direction, however, remains a challenge, because of the thermodynamical equivalence of multiple axis directions on a solid-surface lattice. Here we demonstrate the successful fabrication of an in-plane, unidirectional molecular assembly on graphene. Our methodology relies on nanomechanical symmetry breaking effects under atomic force microscopy tip scanning, which has never been used in molecular alignment. Individual one-dimensional (1D) molecular assemblies were aligned along a selected symmetry axis of the graphene lattice under finely-tuned scanning conditions after removing initially-adsorbed molecules. Experimental statistics and computational simulations suggest that the anisotropic tip scanning locally breaks the directional equivalence of the graphene surface, which enables nucleation of the unidirectional 1D assemblies. Our findings will open new opportunities in the molecular alignment control on various atomically flat surfaces.