A theoretical investigation of the radiative capture of an electron into a bound state of heavy, hydrogen-like ion is presented. Special attention is paid to the question of how the linear polarization of the emitted radiation is affected by the interelectronic interaction effects. An analysis of these effects is performed within both, the screening-potential approximation and the perturbation theory that rigorously treats the electron correlations to the first order in the parameter 1/Z. By making use of these two approaches, detailed calculations are performed for relativistic collisions of hydrogen-like europium Eu62+, bismuth Bi82+, and uranium U91+ ions with free electron and low-Z atomic targets. Results of the calculations indicate that the two-electron effects may significantly influence the polarization properties of the recombination x rays; the effect which can be observed by the present-day polarization detectors.