Spectro-temporal modulations are believed to mediate the analysis of speech sounds in the human primary auditory cortex. Inspired by humans' robustness in comprehending speech in challenging acoustic environments, we propose an intrusive speech intelligibility prediction (SIP) algorithm, wSTMI, for normal-hearing listeners based on spectro-temporal modulation analysis (STMA) of the clean and degraded speech signals. In the STMA, each of 55 modulation frequency channels contributes an intermediate intelligibility measure. A sparse linear model with parameters optimized using Lasso regression results in combining the intermediate measures of 8 of the most salient channels for SIP. In comparison with a suite of 10 SIP algorithms, wSTMI performs consistently well across 13 datasets, which together cover degradation conditions including modulated noise, noise reduction processing, reverberation, near-end listening enhancement, and speech interruption. We show that the optimized parameters of wSTMI may be interpreted in terms of modulation transfer functions of the human auditory system. Thus, the proposed approach offers evidence affirming previous studies of the perceptual characteristics underlying speech signal intelligibility.