  We construct a new classical solution in the ABJM theory corresponding to
M5-branes with a non-zero self-dual three form flux. This is an M-theory lift
of the D4-brane solution expressed as a non-commutative plane in the three
dimensional super Yang-Mills theory. We discuss that our solution is closely
related with the three-algebra. We show that the corresponding configuration of
the M5-brane satisfies the equations of motion in the single M5-brane action.
We find the agreement between the tension of the M5-brane solution in the ABJM
action and the one computed from the single M5-brane action.
