We study the energy loss of magnetic monopoles in a hot plasma and discuss the trapping of magnetic monopoles in the interior of the Sun. We find that magnetic monopoles inpinging onto the Sun with V ∼ 10−3 c are trapped if their mass is M ≲10−16 GeV. Bounds on the flux of such particles are derived from data on the Sun magnetic field, luminosity and neutrino flux. These imply α ≲10−15 cm−2 s−1 sr−1.