The very bright and compact massive young cluster, NGC 3603, has been cited as an example of a starburst in the Milky Way and compared with the much-studied R136/30 Doradus region in the Large Magellanic Cloud. Here we build on the discovery by Mohr-Smith et al. of a large number of reddened O stars around this cluster. We construct a list of 288 candidate O stars with proper motions (PMs), in a region of sky spanning 1.5x1.5deg^2^ centred on NGC 3603, by cross-matching the Mohr-Smith et al. catalogue with Gaia DR2. This provides the basis for a first comprehensive examination of the PMs of these massive stars in the halo of NGC 3603, relative to the much better studied central region. We identify up to 11 likely O star ejections - 8 of which would have been ejected between 0.60 and 0.95Myr ago (supporting the age of ~1Myr that has been attributed to the bright cluster centre). Seven candidate ejections are arranged in a partial ring to the south of the cluster core spanning radii of 9-18arcmin (18-36pc if the cluster is 7kpc away). We also show that the cluster has a halo of a further ~100 O stars extending to a radius of at least 5arcmin, adding to the picture of NGC 3603 as a scaled down version of the R136/30 Dor region.