V606 Centauri (V606 Cen) is an early B-type close binary with an orbital period of 1.4950935 days, and its complete light curves are very difficult to observe on the ground. By analyzing the continuous light curve obtained by TESS, we found that it is a marginal contact binary with a very low fill-out factor of about 2%. The O - C diagram of V606 Cen is constructed for the first time based on 118.8 yr of eclipse times. The O - C diagram has been found to show a downward parabolic change together with a cyclic oscillation with a semiamplitude of 0.0545 days and a period of 88.3 yr. The downward parabolic variation reveals a linear period decrease at a rate of dP/dt = -2.08 x 10(-7) days yr(-1) that can be explained by the mass transfer from the more massive component to the less massive one. Both the marginal contact configuration and the continuous period decrease suggest that V606 Cen is a newly formed contact binary via Case A mass transfer. The cyclic change in the O - C diagram can be explained by the light-travel time effect via the presence of a third body. The lowest mass of the tertiary companion is determined to be M (3) = 4.51 (+/- 0.43) M (circle dot) and the tertiary is orbiting around the central eclipsing binary in a nearly circular orbit (e = 0.33). All of the results indicate that V606 Cen is a newly formed massive contact binary in a hierarchical triple system.