  We consider the focusing fractional nonlinear Schr\"odinger equation \[
i\partial_t u - (-\Delta)^s u = -|u|^\alpha u, \quad (t,x) \in \mathbb{R}^+
\times \mathbb{R}^d, \] where $s \in (1/2,1)$ and $\alpha>0$. By using
localized virial estimates, we establish general blow-up criteria for
non-radial solutions to the equation. As consequences, we obtain blow-up
criteria in both $L^2$-critical and $L^2$-supercritical cases which extend the
results of Boulenger-Himmelsbach-Lenzmann [{\it Blowup for fractional NLS}, J.
Funct. Anal. 271 (2016), 2569--2603] for non-radial initial data.
