In this paper we characterize the Sasakian 3-manifolds admitting β-almost Ricci solitons whose potential vector field is a contact vector field. Among others we prove that a β-almost Ricci soliton whose potential vector field is a contact vector field on a Sasakian 3-manifold is shrinking, Einstein and non-trivial. Moreover, we prove that this type of manifolds are isometric to a sphere of radius √7.