The impacts of climatic change on organisms depend on the interaction of multiple stressors and how these may affect the interactions among species. Consumer—prey relationships may be altered by changes to the abundance of either species, or by changes to the per capita interaction strength among species. To examine the effects of multiple stressors on a species interaction, we test the direct, interactive effects of ocean warming and lowered pH on an abundant marine herbivore (the amphipod Peramphithoe parmerong), and whether this herbivore is affected indirectly by these stressors altering the palatability of its algal food (Sargassum linearifolium). Both increased temperature and lowered pH independently reduced amphipod survival and growth, with the impacts of temperature outweighing those associated with reduced pH. Amphipods were further affected indirectly by changes to the palatability of their food source. The temperature and pH conditions in which algae were grown interacted to affect algal palatability, with acidified conditions only affecting feeding rates when algae were also grown at elevated temperatures. Feeding rates were largely unaffected by the conditions faced by the herbivore while feeding. These results indicate that, in addition to the direct effects on herbivore abundance, climatic stressors will affect the strength of plant—herbivore interactions by changes to the susceptibility of plant tissues to herbivory.