Aseismic crack growth upon activation of fault slip due to fluid injection may or may not lead to the nucleation of a dynamic rupture depending on in-situ conditions, frictional properties of the fault and the value of overpressure. In particular, a fault is coined as unstable if its residual frictional strength $\tau_r$ is lower than the in-situ background shear stress $\tau_o$. We study here how fault dilatancy associated with slip affect shear crack propagation due to fluid injection. We use a planar bi-dimensional model with frictional weakening and assume that fluid flow only takes place along the fault (impermeable rock {/ immature fault}). Dilatancy induces an undrained pore-pressure drop locally strengthening the fault. We introduce an undrained residual fault shear strength $\tau_r^u$ (function of dilatancy) and show theoretically that under the assumption of small scale yielding, an otherwise unstable fault ($\tau_r<\tau_o$) is stabilized when $\tau_r^u$ is larger than $\tau_o$. We numerically solve the complete coupled hydro-mechanical problem and confirm this theoretical estimate. It is important to note that the undrained residual strength is fully activated only if residual friction is reached. Dilatancy stabilizes an otherwise unstable fault if the nucleation of an unabated dynamic rupture -without dilatancy- is affected by residual friction, which is the case for sufficiently large injection pressure. We also discuss the effect of fault permeability increase due to slip. Our numerical results show that permeability increases lead to faster aseismic growth but do not impact the stabilizing effect of dilatancy with respect to dynamic rupture.