We discuss the extension of gauge-invariant electric and magnetic screening masses in the quark-gluon plasma to the case of a finite baryon density, defining them in terms of a matrix of Polyakov loop correlators. We present lattice results for N f ¼ 2 þ 1 QCD with physical quark masses, obtained using the imaginary chemical potential approach, which indicate that the screening masses increase as a function of μ B . A separate analysis is carried out for the theoretically interesting case μ B =T ¼ 3iπ, where charge conjugation is not explicitly broken and the usual definition of the screening masses can be used for temperatures below the Roberge-Weiss transition. Finally, we investigate the dependence of the static quark free energy on the baryon chemical potential, showing that it is a decreasing function of μ B , which displays a peculiar behavior as the pseudocritical transition temperature at μ B ¼ 0 is approached.