Selective Laser-induced Etching (SLE) is a manufacturing process which enables the fabrication of three-dimensional parts from transparent materials with unique freedom of geometry and high precision. First, the outer contour of the part is inscribed in the material using focused ultrashort pulsed laser radiation. Second, the modified design is exposed from the bulk material using wet chemical etching. We analyze the possibility of using SLE for the machining of next generation fused silica ion traps suitable for quantum computing. Such ion traps require an enhanced functionality in combination with reduced error sources and a reproducible manufacturing process. Ion trap designs with three-dimensional features in the micrometer regime are developed to meet these requirements. Challenges of the SLE process arising from the ion trap design and its dimensions are discussed. Different process strategies to fabricate single ion trap components as well as complete ion traps are examined. We demonstrate that next generation ion traps can be machined using SLE and outline the way towards a fabrication on wafer level.