The Zeeman pattern of Mn I lines is sensitive to hyperfine structure (HFS), and because of this, they respond to hectogauss magnetic field strengths differently than the lines commonly used in solar magnetometry. This peculiarity has been employed to measure magnetic field strengths in quiet-Sun regions, assuming the magnetic field to be constant over a resolution element. This assumption is clearly insufficient, biasing the measurements. The diagnostic potential of Mn I lines can be fully exploited only after one understands the sense and magnitude of such bias. We present the first syntheses of Mn I lines in realistic quiet-Sun model atmospheres. The Mn I lines weaken with increasing field strength. In particular, kilogauss magnetic concentrations produce Mn I λ5538 circular polarization signals (Stokes V) that can be up to 2 orders of magnitude smaller than what the weak magnetic field approximation predicts. The polarization emerging from an atmosphere having weak and strong fields is biased toward the weak fields, and HFS features characteristic of weak fields show up even when the magnetic flux and energy are dominated by kilogauss fields. For the HFS feature of Mn I λ5538 to disappear, the filling factor of kilogauss fields has to be larger than the filling factor of subkilogauss fields. Since the Mn I lines are usually weak, Stokes V depends on magnetic field inclination according to the simple cosine law. Atmospheres with unresolved velocities produce very asymmetric line profiles, which cannot be reproduced by simple one-component model atmospheres. Using the HFS constants available in the literature, we reproduce the observed line profiles of nine lines with varied HFS patterns.