  We compute the entanglement entropy of the Wilson-Fisher conformal field
theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$
for general entanglement geometries. We show that the leading large $N$ result
can be obtained from the entanglement entropy of $N$ Gaussian scalar fields
with their mass determined by the geometry. For a few geometries, the universal
part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT
of $N$ massless scalar fields. However, in most cases, these CFTs have a
distinct universal entanglement entropy even at $N=\infty$. Notably, for a
semi-infinite cylindrical region it scales as $N^0$, in stark contrast to the
$N$-linear result of the Gaussian fixed point.
