State-of-the-art fabrication and characterization techniques are nowadays able to experimentally control light-matter interaction at sub-nanometer scales. Thus, theoretical schemes able to overcome the limits of the classical vision and to fully take into account quantum mechanical effects are needed. In this work, we propose time-dependent density functional tight-binding (TD-DFTB) as a new workhorse for computational quantum plasmonics. DFTB has been demonstrated to be an efficient scheme for describing the structural, electronic, and optical properties of different biomolecules and carbon-based nanosystems. We report here on the absorption spectra of silver tetrahedral closed-shell Ag_n clusters within the framework of TD-DFTB and on their comparison with the reference ones, obtained within the first-principles time-dependent density functional theory (TD-DFT) scheme. It is found out that, under an appropriate choice of the Slater-Koster parametrization, optical spectra result to be in a very good agreement with the reference ones and achievable within a total wall time less than 0.2% the TD-DFT one. This result offers a firm basis to overcome the bottleneck of computational cost in plasmonics and paves the way toward future developments in quantum plasmonics.