  We study a $(3+1)$-dimensional $U(N)$ gauge theory with $N$-flavor
fundamental scalar fields, whose color-flavor locked (CFL) phase has
topologically stable non-Abelian vortices. The $U(1)$ charge of the scalar
fields must be $Nk+1$ for some integer $k$ in order for them to be in the
representation of $U(N)$ gauge group. This theory has a $\mathbb{Z}_{Nk+1}$
one-form symmetry, and it is spontaneously broken in the CFL phase, i.e., the
CFL phase is topologically ordered if $k\not=0$. We also find that the world
sheet of topologically stable vortices in CFL phase can generate this one-form
symmetry.
