Elucidating how individual mutations affect the protein energy landscape is crucial for understanding how proteins evolve. However, predicting mutational effects remains challenging because of epistasis-the nonadditive interactions between mutations. Here, we investigate the biophysical mechanism of strain-specific epistasis in the nonstructural protein 1 (NS1) of influenza A viruses (IAVs). We integrate structural, kinetic, thermodynamic, and conformational dynamics analyses of four NS1s of influenza strains that emerged between 1918 and 2004. Although functionally near-neutral, strain-specific NS1 mutations exhibit long-range epistatic interactions with residues at the p85β-binding interface. We reveal that strain-specific mutations reshaped the NS1 energy landscape during evolution. Using NMR spin dynamics, we find that the strain-specific mutations altered the conformational dynamics of the hidden network of tightly packed residues, underlying the evolution of long-range epistasis. This work shows how near-neutral mutations silently alter the biophysical energy landscapes, resulting in diverse background effects during molecular evolution.