Magnetic resonances not only play crucial roles in artificial magnetic materials but also offer a promising way for light control and interaction with matter. Recently, magnetic resonance effects have attracted special attention in plasmonic systems for overcoming magnetic response saturation at high frequencies and realizing high-performance optical functionalities. As novel states of matter, topological insulators (TIs) present topologically protected conducting surfaces and insulating bulks in a broad optical range, providing new building blocks for plasmonics. However, until now, high-frequency (e.g. visible range) magnetic resonances and related applications have not been demonstrated in TI systems. Herein, we report for the first time, to our knowledge, a kind of visible range magnetic plasmon resonances (MPRs) in TI structures composed of nanofabricated Sb2Te3 nanogrooves. The experimental results show that the MPR response can be tailored by adjusting the nanogroove height, width, and pitch, which agrees well with the simulations and theoretical calculations. Moreover, we innovatively integrated monolayer MoS2 onto a TI nanostructure and observed strongly reinforced light–MoS2 interactions induced by a significant MPR-induced electric field enhancement, remarkable compared with TI-based electric plasmon resonances (EPRs). The MoS2 photoluminescence can be flexibly tuned by controlling the incident light polarization. These results enrich TI optical physics and applications in highly efficient optical functionalities as well as artificial magnetic materials at high frequencies.