A zero-force member in neither in compression nor tension. Consideration of zero-force members is usually reserved for pin-connected truss analysis (using Method of Joints).
In general, when drawing a free-body diagram of any individual member (or isolating a pinned joint) in a structural truss system, the joint or member in question needs to be “in equilibrium,” that is, all forces acting on the joint or member need to balance, or cancel each other out (vertical, horizontal forces, applied moments). By summing moments (about any point on a member), or summing forces on a pinned joint, equilibrium is established and should be equal to zero.
During analysis, should a joint have a single force acting on it which cannot be balanced by a corresponding and opposite force, that member initiating that force is considered a zero-force member.