A method of performing a squeeze treatment comprises pumping a treatment fluid under pressure through a wellbore into a subterranean formation, wherein the treatment fluid includes a hydrogen sulfide scavenging compound that adsorbs onto the subterranean formation in a region around the wellbore. Production fluids are then allowed to flow from the subterranean formation into the wellbore, wherein the production fluids contact the adsorbed hydrogen sulfide scavenging compound as the production fluids flow through the region around the wellbore, and wherein the production fluids contain hydrogen sulfide that reacts with the hydrogen sulfide scavenging compound to reduce an amount of hydrogen sulfide in the production fluids before the production fluids flow into the wellbore.