Black, air-stable crystals of the new ruthenate(V) Sr₃(Ag_2/3Sr_1/6)RuO₆ were grown in a silver ampoule using KO₂ as oxidative flux. X-ray diffraction on single-crystals revealed a rhombohedral structure with the space group R (Formula presented.) c. Sr₃(Ag_2/3Sr_1/6)RuO₆ crystallizes isostructural to Sr₄PtO₆ in the K₄CdCl₆ structure type. By sharing trigonal faces, alternating [RuO₆] octahedra and [(Ag_2/3Sr_1/6□_1/6)O₆ trigonal prisms form segmented chains running parallel to the crystallographic c-axis. Eightfold coordinated strontium cations are located between the rods. Regardless of the wide spatial separation of the magnetic cations (588 and 594 pm), Sr₃(Ag_2/3Sr_1/6)RuO₆ shows long-range antiferromagnetic order below the relatively high Néel temperature of 79 K in magnetic fields up to at least 9 T, as measurements of the magnetic susceptibility and heat capacity show. Despite the pseudo one-dimensional character of the structure, the characteristic of the susceptibility indicates a three-dimensional coupling of magnetic ions.