We investigated changes in the shape of tubular ternary vesicles induced by phase separation into liquid-ordered and liquid-disordered phases. Tubular vesicles transform into two types of periodically modulated vesicles depending on the area fraction of the liquid-ordered phase. One type is a necklace of oblate subunits with two circular domains of the liquid-order phase, and the other is a periodically modulated tube with stripes of the liquid-order phase. The transition between the circular and striped domains is governed by the domain boundary energy, whereas the periodicity of modulated vesicles is determined geometrically based on the fixed volume and area constraints. The observed multidomain vesicles are kinetically trapped in metastable states, and all domains show budding to reduce the boundary energy.