Nematicity is ubiquitous in electronic phases of high-Tc superconductors, particularly in the Fe-based systems. While several experiments have probed nematic fluctuations, they have been restricted to uniform or momentum averaged fluctuations. Here, we investigate the behavior of finite-momentum nematic fluctuations by utilizing the anomalous softening of acoustic phonon modes in optimally doped Ba(Fe0.94Co0.06)2As2. We determine the nematic correlation length and find that it sharply changes its T-dependence at Tc, revealing a strong connection between nematicity and superconductivity.