Magnetotransport of individual rolled-up Fe ₃Si nanomembranes is investigated in a broad temperature range from 4.2 K up to 300 K in pulsed magnetic fields up to 55T. The observed magnetoresistance (MR) has the following pronounced features: (i) MR is negative in the investigated intervals of temperature and magnetic field; (ii) its magnitude increases linearly with the magnetic field in a low-field region and reveals a gradual trend to saturation when the magnetic field increases; (iii) the MR effect becomes more pronounced with increasing temperature. These dependences of MR on the magnetic field and temperature are in line with predictions of the spin-disorder model of the spin-flip sd interaction assisted with creation or annihilation of magnons, which is expected above a certain critical temperature. Comparison of the MR features in rolled-up and planar samples reveals a substantial increase of the critical temperature in the rolled-up tube, which is attributed to a new geometry and internal strain arising in the rolled-up nanomembranes, influencing the electronic and magnetic properties of the material.