XMM-Newton observed the soft gamma repeater SGR 1806-20 about two months after its 2004 December 27 giant flare. A comparison with the previous observations taken with the same instrument in 2003-2004 shows that the pulsed fraction and the spin-down rate have significantly decreased and that the spectrum slightly softened. These changes may indicate a global reconfiguration of the neutron star magnetosphere. The spectral analysis confirms that the presence of a blackbody component in addition to the power-law is required. Since this additional component is consistent with being constant with respect to the earlier observations, we explore the possibility of describing the long-term spectral evolution as only due to the power-law variations. In this case, the slope of the power-law does not significantly change and the spectral softening following the giant flare is caused by the increase of the relative contribution of the blackbody over the power-law component.