We study here the special decay properties of real solutions to the initial value problem associated with the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation. More precisely, we prove the properties of exponential decay of order $3/2$ above the plane $x+y+z=0$ as time evolves. This property is related with the persistence properties of the solution flow in weighted Sobolev spaces and sharp unique continuation properties of solutions to this problem.