We present results from the first successful millimetre (combined 33 and 35 GHz) observations of the neutron star X-ray binary Circinus X-1, using the Australia Telescope Compact Array. The source was clearly detected in all three observing epochs. We see strong evidence for a periastron flare beginning at MJD 55519.9 ± 0.04 with estimated peak flux densities of up to 50 mJy and which proceeds to decline over the following 4 d. We directly resolve jet structures on sub-arcsecond scales. Flux density variability and distance from the core of nearby components suggest recent shock re-energization, though we are unable to directly connect this with the observed flare. We suggest that, if the emission is powered by an unseen outflow, then a phase delay exists between flare onset and subsequent brightening of nearby components, with flows reaching mildly relativistic velocities. Given resolved structure positions, in comparison to past observations of Cir X-1, we find evidence that jet direction may vary with distance from the core, or the source’s precession parameters have changed.