We report on the discovery of ionised gas filaments in the circum-galactic halo of the extremely metal-poor compact starburst SBS 0335-052E in a 1.5 h integration with the MUSE integral-field spectrograph. We detect these features in H alpha and [O III] emission down to a limiting surface-brightness of 5 x 10(-19) erg s(-1) cm(-2) arcsec(-2). The filaments have projected diameters of 2.1 kpc and extend more than 9 kpc to the north and north-west from the main stellar body. We also detect extended nebular He II lambda 4686 emission that brightens towards the north-west at the rim of a starburst driven super-shell. We also present a velocity field of the ionised gas. The filaments appear to connect seamlessly in velocity space to the kinematical disturbances caused by the shell. Similar to high-z starforming galaxies, the ionised gas in this galaxy is dispersion dominated. We argue that the filaments were created via feedback from the starburst and that these ionised structures in the halo may act as escape channels for Lyman continuum radiation in this gas-rich system.