The magnetic field observations by the Mars Global Surveyor (MGS) performed on the premapping orbits in the years 1997–1998 in the low-altitude ionosphere of Mars show the existence of a strong ’external’ magnetization not related to the ’internal’ crustal magnetization. A significant increase of the magnetic field strength is observed in the collisional northern ionosphere, at altitudes of ~200 km and at 60°–90° solar zenith angles sampled by MGS. The magnetization features and the magnetic field topology vary significantly with the sector structure of the interplanetary magnetic field (IMF). For ByIMF > 0 the magnetic flux tubes transported to altitudes of ~200 km are suddenly straightened releasing their tangential stresses. For ByIMF < 0 a rotation of the magnetic field vector by almost 180° occurs. Such an asymmetry in the ionospheric response on Mars is similar to the asymmetry observed on Venus at the periods of low solar activity indicating its universal origin for magnetized ionospheres. It is suggested that the electric currents generated in the collisional ionosphere where the ions become demagnetized while the electrons remain magnetized produce the observed features.