Using a data set corresponding to an integrated luminosity of $3 fb^{-1}$, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV, the effective lifetime in the $B^0_s rightarrow J/psi eta$ decay mode, $tau_{textrm{eff}}$, is measured to be $tau_{textrm{eff}} = 1.479 pm 0.034~textrm{(stat)} pm 0.011 ~textrm{(syst)}$ ps. Assuming $CP$ conservation, $tau_{textrm{eff}}$ corresponds to the lifetime of the light $B_s^0$ mass eigenstate. This is the first measurement of the effective lifetime in this decay mode.