The removal of a widespread used drug (i.e., ibuprofen) from water was investigated using high valuable carbon adsorbents obtained from chemical and physical activation of a bioresource (cork) and a municipal waste (plastic). The waste-derived carbons outperformed the adsorption capacity of commercial carbonaceous adsorbents due to their adequate features for the removal of the targeted compound. Regarding the adsorption mechanism, the results obtained point out that ibuprofen retention is favored in activated carbons with basic surface properties. On the other hand, the textural features also play an important role; the presence of a transport pores network (i.e., mesopores) is crucial to ensure the accessibility to the inner porosity, and the microporosity must be large enough to accommodate the ibuprofen molecule. Specifically, adsorbents with a large fraction of ultramicropores (pore widths <0.7 nm) are not adequate to effectively remove ibuprofen.