Mercury is a highly toxic pollutant of major public health concern, and human exposure is mainly related to the aqueous phase, where its dominant form is methyl-mercury (MeHg). In the current work, two carbon-based adsorbents, i.e., a commercial activated carbon and a sunflower seeds’ biochar, were modified by the introduction of thiol-active groups onto their surfaces for the MeHg removal from natural-like water in ppb concentration levels. The examined thiol-functionalization was a two-step process, since the raw materials were initially treated with nitric acid (6 N), which is a reagent that favors the formation of surface carboxyl groups, and subsequently by the thiol surface bonding groups through an esterification reaction in methanol matrix. The adsorbents’ capacity was evaluated toward the Hgtotal legislative regulation limit (1 μg/L) in drinking water (denoted as Q1). The respective isothermal adsorption results revealed an increased affinity between MeHg and thiol-functionalized materials, where the commercial carbon showed slightly higher capacity (0.116 μg Hg/mg) compared with the biochar (0.108 μg Hg/mg). This variation can be attributed to the respective higher surface area, resulting, also, to higher thiol groups loading. Regarding the proposed mechanism, it was proved that the S-Hg bond was formed, based on the characterization of the best performed saturated adsorbent.