Wave phenomena in bianisotropic media have been broadly scrutinized in classical electrodynamics, as these media offer additional degrees of freedom to engineer electromagnetic waves. However, all investigations concerning such systems have so far been limited to stationary (time-invariant) media. Temporally varying the magnetoelectric coupling manifesting bianisotropy engenders a unique prospect to manipulate wave-matter interactions in new ways. In this paper, we theoretically contemplate electromagnetic effects in weakly dispersive bianisotropic media of all classes when the corresponding magnetoelectric coupling parameter suddenly jumps in time, creating a time interface in spatially uniform bianisotropic media. We investigate scattering effects at such time interfaces, revealing novel polarization- and direction-dependent phenomena. We anticipate that our work paves the road for further exploration of time-varying bianisotropic metamaterials (metasurfaces) and bianisotropic photonic time crystals, thus opening up interesting possibilities to control wave polarization and amplitude in reciprocal and nonreciprocal manners.