Under applied stress, the viscosity of many dense particulate suspensions increases drastically, a response known as discontinuous shear-thickening (DST). In some cases, the applied stress can even transform the suspension into a solid-like shear jammed state. Although shear jamming (SJ) has been probed for dense suspensions with particles having well-defined shapes, such a phenomenon for fractal objects has not been explored. Here, using rheology and in situ optical imaging, we study the flow behaviour of ultra-dilute fractal suspensions of multi-walled carbon nanotubes (MWCNT) under confinement. We show a direct transition from flowing to SJ state without a precursory DST in fractal suspensions at an onset volume fraction, ϕ ∼ 0.5%, significantly lower than that of conventional dense suspensions (ϕ ∼ 55%). The ultra-low concentration enables us to demonstrate the fragility and associated contact dynamics of the SJ state, which remain experimentally unexplored in suspensions. Furthermore, using a generalized Wyart–Cates model, we propose a generic phase diagram for fractal suspensions that captures the possibility of SJ without prior DST over a wide range of shear stress and volume fractions.