ABSTRACT We use a fully GPU N-body code to demonstrate that dark matter (DM) minihaloes, as a new component of globular clusters (GCs), resolve both the timing and cusp–core problems in Fornax if the (five or six) GCs were recently accreted (≤3 Gyr ago) by Fornax. Under these assumptions, infall of these GCs does not occur and no star clusters form in the centre of Fornax in accordance with observations. We find that crossings of GCss that have DM minihaloes near the Fornax centre induce a cusp-to-core transition of the DM halo and hence resolve the cusp–core problem in this dwarf galaxy. The DM core size depends on the frequency of GC crossings. Our simulations clearly demonstrate also that between the passages, the DM halo can regenerate its cusp. Moreover, our models are in good agreement with constraints on the DM masses of GCs as our clusters lose a large fraction of their initial DM minihaloes. These results provide circumstantial evidence for the universal existence of DM haloes in GCs.