We investigate the formation of polarization profiles induced by a magnetic field in the He I multiplet at 10830 Å. Our analysis considers the Zeeman splitting in the incomplete Paschen-Back regime. The effects turn out to be important and produce measurable signatures on the profiles, even for fields significantly weaker than the level-crossing field (~400 G). When compared to profiles calculated with the usual linear Zeeman effect, the incomplete Paschen-Back profiles exhibit the following conspicuous differences: (1) a non-Doppler blueshift of the Stokes V zero-crossing wavelength of the blue component; (2) area and peak asymmetries, even in the absence of velocity and magnetic gradients; and (3) a ~25% reduction in the amplitude of the red component. These features do not vanish in the weak-field limit. The spectral signatures that we analyze in this paper may be found in previous observations published in the literature.