Electrospun filaments represent a new generation of medical textiles with promising applications in soft tissue repair. A potential strategy to improve their design is to combine them with bioactive molecules. Curcumin, a natural compound found in turmeric, is particularly attractive for its antioxidant, anti-inflammatory, and antimicrobial properties. However, investigating the range of relevant doses of curcumin in materials designed for tissue regeneration has remained limited. In this paper, a wide range of curcumin concentrations was explored and the potential of the resulting materials for soft tissue repair applications was assessed. Polydioxanone (PDO) filaments were prepared with various amounts of curcumin: 0%, 0.001%, 0.01%, 0.1%, 1%, and 10% (weight to weight ratio). The results from the present study showed that, at low doses (≤0.1%), the addition of curcumin has no influence on the spinning process or on the physicochemical properties of the filaments, whereas higher doses lead to smaller fiber diameters and improved mechanical properties. Moreover, filaments with 0.001% and 0.01% curcumin stimulate the metabolic activity and proliferation of normal human dermal fibroblasts (NHDFs) compared with the no-filament control. However, this stimulation is not significant when compared to the control filaments (0%). Highly dosed filaments induce either the inhibition of proliferation (with 1%) or cell apoptosis (with 10%) as a result of the concentrations of curcumin found in the medium (9 and 32 μM, respectively), which are near or above the known toxicity threshold of curcumin (~10 μM). Moreover, filaments with 10% curcumin increase the catalase activity and glutathione content in NHDFs, indicating an increased production of reactive oxygen species resulting from the large concentration of curcumin. Overall, this study suggested that PDO electrospun filaments loaded with low amounts of curcumin are more promising compared with higher concentrations for stimulating tissue repair. This study also highlighted the need to explore lower concentrations when using polymers as PDO, such as those with polycaprolactone and other degradable polyesters.