Context. A key science goal of the Gaia-ESO survey (GES) at the VLT is to use the kinematics of low-mass stars in young clusters and star forming regions to probe their dynamical histories and how they populate the field as they become unbound. The clustering of low-mass stars around the massive Wolf-Rayet binary system γ 2 Velorum was one of the first GES targets. Aims. To empirically determine the radial velocity precision of GES data, construct a kinematically unbiased sample of cluster members and characterise their dynamical state. Methods. Targets were selected from colour-magnitude diagrams and intermediate resolution spectroscopy was used to derive radial velocities and assess membership from the strength of the Li i 6708Å line. The radial velocity distribution was analysed using a maximum likelihood technique that accounts for unresolved binaries. Results. The GES radial velocity precision is about 0.25 kms − 1 and su ffi cient to resolve velocity structure in the low-mass population around γ 2 Vel. The structure is well fitted by two kinematic components with roughly equal numbers of stars; the first has an intrinsic dispersion of 0 . 34 ± 0 . 16 km s − 1 , consistent with virial equilibrium. The second has a broader dispersion of 1 . 60 ± 0 . 37 km s − 1 and is o ff set from the first by ≃ 2 km s − 1 . The first population is older by 1–2 Myr based on a greater level of Li depletion seen among its M-type stars and is probably more centrally concentrated around γ 2 Vel. Conclusions. We consider several formation scenarios, concluding that the two kinematic components are a bound remnant of the original, denser cluster that formed γ 2 Vel, and a dispersed population from the wider Vela OB2 association, of which γ 2 Vel is the most massive member. The apparent youth of γ 2 Vel compared to the older ( ≥ 10 Myr) low-mass population surrounding it suggests a scenario in which the massive binary formed in a clustered environment after the formation of the bulk of the low-mass stars.