Thanks to their unique nanoscale properties, nanomedicines can overcome some of the shortcomings of conventional therapies. For better predictive screening, it is important to assess their performance in three-dimensional (3D) multicellular tumour spheroids (MCTS) that can recapitulate the physiological barriers found in real tumours. Today, the evaluation of drug delivery nanosystems in MCTS is mainly explored by means of microscopy techniques that are invasive and require fluorescent labels which modify the composition and fate of the carriers. In recent years, a new quantitative microscopy technique based on Brillouin light scattering (BLS) has been proposed that uses the interaction of laser light with picosecond timescale density fluctuations in the sample. Because it is label-free, all-optical and non-destructive, BLS has gained interest in the pharmaceutical and biomedical fields. In this work, we implemented a fast BLS spectrometer and used the Brillouin frequency shift at the center of the MCTS as a quantitative readout for drug efficacy. We first investigated the ability of this setup to quantify drug efficacy in MCTS grown in classical multiwell plates and concluded that the low number of samples available in the multiwells limits the statistical significance of the results. To improve the throughput, we then combined the microscope with agarose microwells designed to fabricate a large number of MCTS and test 50 MCTS in less than a minute. Using this platform, we assessed the efficacy of polymeric nanoparticles (NPs) loaded with a platinum derivative anticancer drug (dichloro(1,2-diaminocyclohexane)platinum(II)) in reducing the growth of colorectal cancer cells (HCT-116) in MCTS. We observe a time- and dose-dependent decrease in the frequency shift, revealing the progressive loss of mechanical integrity in the MCTS. These results demonstrate that BLS probing of MCTS grown in agarose microwells is a promising tool for high-throughput screening of nanocarriers in 3D models.