  We study intersecting noncommutative (NC) M5-branes from \kappa-invariance of
an open supermembrane action with constant three-form fluxes. The
$\kappa$-invariance gives rise to possible D-brane configurations for which
projection operators can be determined. We construct projection operators for
two types of 1/4 BPS intersecting NC M5-branes. The one is an intersection of
two NC M5-branes: NC M5\bot NC M5 (3). The other is that of a NC M5-brane and a
commutative (C) M5-brane: NC M5\bot C M5 (1). A NC M5-brane can be viewed as a
bound state of M5 and M2, and the configurations M2\bot M5 (1) and M2\bot M2
(0) are realized on the intersecting M5-branes. Taking a commutative limit the
allowed intersecting M5-branes are surely reproduced: M5\bot M5 (3) and M5\bot
M5 (1).
