We investigate the nonequilibrium tube length fluctuations during the relaxation of an initially stretched, entangled polymer chain. The time-dependent variance sigma (2) of the tube length follows in the early-time regime a simple universal power law sigma (2) = A roott originating in the diffusive motion of the polymer segments. The amplitude A is calculated analytically both from standard reptation theory and from an exactly solvable lattice gas model for reptation and its dependence on the initial and equilibrium tube length, respectively, is discussed. The nonuniversality suggests the measurement of the fluctuations (e.g., using flourescence microscopy) as a test for reptation models.