Mass is a defining property of particles, shaping their fundamental nature and interactions. In condensed matter systems, the effective mass of electrons has long been regarded as a key factor influencing material properties, including their transport and optical responses. In this work, we challenge this conventional wisdom by unveiling a mass-invariant universal optical conductivity, purely derived from quantum geometry, in quadratic band-touching semimetals. Specifically, the optical conductivity simplifies to σ = (e²/8ℏ)d²max, independent of effective mass and other band structure details, where dmax represents the maximum Hilbert-Schmidt quantum distance. Furthermore, under time-reversal and rotational symmetries, dmax is restricted to discrete values of 0 or 1, leading to a quantized universal optical conductivity. % We also use first principles calculations to demonstrate the mass-invariant universal optical conductivity across multiple materials, including bilayer graphene, monolayer bismuth, monolayer kagome Pd₃P₂S₈, and other realistic material candidates. % Our work establishes a new class of universal quantities in quantum materials entirely governed by quantum geometry.