Magnetic properties of dirty multiband superconductors near the upper critical field are studied. The parameter kappa(2) characterizing magnetization slope is shown to have a significant temperature variation which is quite sensitive to the pairing interactions and relative strengths of intraband impurity scattering. In contrast to single-band superconductors the increase of kappa(2) at low temperatures can be arbitrarily large determined by the ratio of maximal and minimal diffusion coefficients in different bands. Temperature dependencies of kappa(2)(T) in two-band MgB2 and iron-based superconductors are shown to be much more sensitive to the multiband effects than the upper critical field H-c2(T).