The field-induced dynamics of polarons in armchair graphene nanoribbons (GNRs) is theoretically investigated in the framework of a two-dimensional tight-binding model with lattice relaxation. Our findings show that the semiconductor behavior, fundamental to polaron transport to take place, depends upon of a suitable balance between the GNR width and the electronphonon (eph) coupling strength. In a similar way, we found that the parameter space for which the polaron is dynamically stable is limited to an even narrower region of the GNR width and the eph coupling strength. Interestingly, the interplay between the external electric field and the eph coupling plays the role to define a phase transition from subsonic to supersonic velocities for polarons in GNRs.