We assume that there is gluon condensate in the zero-momentum mode in the QCD ground state. A lowest-order calculation in terms of a condensate order parameter leads to a dynamical mass for gluons via the Schwinger mechanism and a gluon propagator with no on-mass-shell singularities — that is, the gluon is a "nonpropagating mode" in the gluon condensate. We transform our momentum-space propagator into coordinate space and find that the propagator has essentially the same delta-function light-cone singularities as the free propagator. However, in contrast to a theory without confinement, we show that the propagator exhibits exponential decay, both for time-like and space-like propagation. In this manner, we obtain a space-time characterization of the confinement phenomenon in terms of an order parameter of the condensate.