Abstract In this paper, we study the next-to-leading order corrections in the mass multipole expansion, i.e. the mass octupole and current quadrupole, to gravitational wave production by close hyperbolic encounters of compact objects. We find that the signal is again, as in the simple quadrupole case, a burst event with the majority of the released energy occurring during the closest approach. In particular, we investigate the relative contribution to the power, both in the time and frequency domains, and total energy emitted by each order in the mass multipole expansion in gravitational waves. To do so, we include in the quadrupole term its first order post-Newtonian correction, giving this a contribution to the power of the same order as that of the mass octupole and the current quadrupole. We find specific configurations of systems where these corrections could be important and should be taken into account when analysing burst events.