The generation and propagation of a packet of small-amplitude inertia–gravity waves (IGWs) in a rotating stratified balanced flow is described. The initially balanced geophysical flow is an unstable baroclinic jet which breaks up into a street of cyclonic and anticyclonic vortices. The small-amplitude unbalanced component of the flow is extracted from the large-amplitude mesoscale balanced flow using the optimal potential vorticity balance approach. This analysis reveals that during the instability the balanced flow spontaneously emits bursts of IGWs. The emission occurs along two directions, into and out of the anticyclonic vortices. The inward-waves remain trapped inside the vortices while the outward-waves propagate away from them as a packet of small-amplitude IGWs with a three-dimensional helical structure. The wave packet emission is confirmed for different spatial resolutions ($128^3$, $160^3$, $192^3$ and $256^3$ grid points). The ratio between the balanced vertical and horizontal velocity components is of the order of $10^{-3}$, as is typical of mesoscale geophysical flows. The ratio between the unbalanced vertical and horizontal components is about 0.1. Since the unbalanced horizontal and the balanced vertical velocity components are of similar magnitude, the vertical velocity of the IGWs is about $10^{-4}$ times the balanced horizontal velocity. The IGWs are dominated by frequencies close to the inertial frequency and have a clockwise-rotating horizontal velocity, similar to plane wave solutions.