This investigation is devoted to the study of the viscoelastic behavior of human abdominal fascia from the umbilical region. Seventeen samples 10 mm wide and up to 70 mm long were cut along the primary fiber direction (group FL) or perpendicular to it (group FT) and subjected to relaxation tests. The viscoelastic response of the tissue at three different strain levels (4%, 5%, and 6%) was investigated. The relaxation curves were fitted using a two-stage decaying exponential form. The following parameters were determined: initial stress σ0, relaxation times τ1 and τ2, stress reduction Δσ, initial relaxation modulus E and equilibrium relaxation modulus Eeq, as well as the ratio E/Eeq. Fiber orientation and strain levels were varied to determine their influence on the viscoelastic properties of fascia. The results highlight the inherent viscoelastic mechanical properties of umbilical fascia. The values of the viscoelastic parameters determined for the longitudinal and transverse directions varied markedly. Significant differences were found between the two groups FL and FT for the initial stress at 5% and 6% strain (p < 0.038) and for the initial and equilibrium moduli at the 6% strain level (p < 0.046). The stress reduction in samples from the FL group (45–55%) was less than that in samples from the FT group (37–54%), but this difference was not significant (p > 0.388). The influence of strain level on the parameter values was not statistically significant (p > 0.121). The nonlinear response of the tissue was demonstrated over the chosen strain range.