For a competition-diffusion blow-up system involving the fractional Laplacian of the form

$-(-\Delta)^su=uv^2,\quad-(-\Delta)^sv=vu^2,\quad u,v>0 \ \mathrm{in} \ \mathbb{R}^N,$

whith $s\in(0,1)$, we prove that the maximal asymptotic growth rate for its entire solutions is $2s$; that is,

$u(x)+v(x)\leq c\left(1+|x|^2\right)^{s}.$

Moreover, since we are able to construct symmetric solutions to the problem, when $N=2$ with prescribed growth arbitrarily close to the critical one, we can conclude that the asymptotic bound found is optimal.