The prospects to study hyperon-nuclei/nucleon interactions at BESIII and similar $e^+ e^-$ colliders are proposed in this work. Utilizing the large quantity of hyperons produced by the decay of 10 billion $J/\psi$ and 2.7 billion $\psi(3686)$ collected at BESIII, the cross sections of several specific elastic or inelastic hyperon-nuclei reactions can be measured via the scattering between the hyperons and the nucleus in the dense objects of BESIII detector. Subsequently, the cross sections of corresponding hyperon-nucleon interactions are able to be extracted with further phenomenological calculation. Furthermore, the interactions between antihyperon and nuclei/nucleon, including scattering and annihilation, can also be studied via the method proposed in this paper. The results will definitely benefit a lot the precise probe of the hyperon-nuclei/nucleon interactions and provide constraints for the studies of the potential of strong interaction, the origin of color confinement, the unified model for baryon-baryon interactions, and the internal structure of neutron stars. In addition, the desirable prospects of corresponding studies in the future Super Tau-Charm Factory (STCF) are discussed and estimated in this work. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.