We examine the wave-induced mean flow of a small-amplitude, quasi-monochromatic, three-dimensional Boussinesq internal gravity wave-packet in a uniformly stratified ambient. It has been known since Bretherton (1969) that two-dimensional and three-dimensional wave packets induce fundamentally different flows. Whereas the wave-induced mean flow for compact three-dimensional wavepackets consists of a purely horizontal localized circulation that translates with and around the wavepacket, such a flow is prohibited for a two dimensional wavepacket of infinite spanwise extent, which instead induces a non-local internal wave response that is long compared with the streamwise-extent of the wavepacket. Through perturbation expansions supplemented with numerical simulations, we show that wide three-dimensional wavepackets induce both horizontal circulations as well as long internal waves. The latter become significant if the spanwise extent of the wavepacket is an order of magnitude larger than its vertical extent. We derive an approximate formula for the aspect ratio of the wavepacket at which the induced flows associated with the horizontal circulation and long waves are predicted to be of the same order of magnitude.