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The dynamical properties of soliton and vortex are closely related to the spontaneous symmetry breaking and the intertwining between internal and external degrees of freedom. We investigate the dynamics of ring dark solitons in a two-component Bose–Einstein condensate with nonlocal Rydberg interaction, where the continuous rotational symmetry is broken. Our results show that the dynamics of such a system, including the ring dark soliton and the vortices followed by the collapse of ring dark soliton, show strong dependence on the strength of nonlocal Rydberg interaction. It is shown that the radius, at which the snake instability of ring dark solitons occurs, increases with the Rydberg interaction, indicating a shorter lifetime. We also observe a critical value of the nonlocal Rydberg interaction, below which the number of vortex pair decreases with the Rydberg interaction, while no visible vortices generated above such critical value. • The dynamics of ring dark soliton with nonlocal Rydberg interaction is considered. • Two classes of novel dynamics of the followed vortices are predicted. • The critical value of nonlocal Rydberg interaction for the generation of vortices is discussed. [ABSTRACT FROM AUTHOR]