[en] ⁵⁷Fe Moessbauer spectroscopy was applied to an iron-based layered superconductor LaFeAsO_0.89F_0.11 with a transition temperature of 26 K and to its parent material LaFeAsO. Throughout the temperature range from 4.2 to 298 K, a singlet pattern with no magnetic splitting was observed in the Moessbauer spectrum of the F-doped superconductor. Furthermore, no additional internal magnetic field was observed for the spectrum measured at 4.2 K under a magnetic field of 7 T. On the other hand, magnetically split spectra were observed in the parent LaFeAsO below 140 K, and this temperature is slightly lower than that of a structural phase transition from tetragonal to orthorhombic phase, which accompanies the electrical resistivity anomaly at around 150 K. The magnetic moment is estimated to be ∼0.35 μ_B/Fe from the internal magnetic field of 5.3 T at 4.2 K in the orthorhombic phase, and the spin disorder appears to remain in the magnetically ordered state even at 4.2 K. The lack of a magnetic transition in LaFeAsO_0.89F_0.11 down to 4.2 K suggests that this system exhibits a paramagnetic state or that the magnetic moment is small. The present results show that F doping effectively suppresses the magnetic and structural transitions in the parent material, leading to the emergence of superconductivity in the F-doped system. (author)