We present the first measurement of the Σ beam asymmetry in η photoproduction on the neutron in the photon energy range from threshold to 1.5 GeV. Data have been collected by using the tagged and linearly polarized photon beam and the large solid angle apparatus of the GRAAL facility. Neutron data have been selected among η photoproduction events on the deuteron in the quasi-free kinematics approximation. Proton data, extracted in the same way, are within errors identical to those previously obtained on free protons at the GRAAL facility, except for a few points falling in certain energy bins. This difference is, however, well understood in terms of the Fermi motion of the nucleons in the deuteron. We take the consistency of free and quasi-free proton data as an indication that nuclear effects are negligible also for neutron data. The ETAMAID model, in which a strong coupling of the D15(1675) resonance to the η-neutron channel is introduced, can explain the proton data very well, but it cannot describe the beam asymmetry for the neutron.