Demand-side restrictions on high-deforestation commodities are expanding as a climate policy, but their impact on reducing tropical deforestation and emissions has yet to be quantified. Here we model the effects of demand-side restrictions on high-deforestation palm oil in Europe on deforestation and emissions in Indonesia. We do so by integrating a model of global trade with a spatially explicit model of land-use change in Indonesia. We estimate a European ban on high-deforestation palm oil from 2000 to 2015 would have led to a 8.9% global price premium on low-deforestation palm oil, resulting in 21 374 ha yr−1 (1.60%) less deforestation and 21.1 million tCO2 yr−1 (1.91%) less emissions from deforestation in Indonesia relative to what occurred. A hypothetical Indonesia-wide carbon price would have achieved equivalent emission reductions at $0.81/tCO2. Impacts of a ban are small because: 52% of Europe's imports of high-deforestation palm oil would have shifted to non-participating countries; the price elasticity of supply of high-deforestation oil palm cropland is small (0.13); and conversion to oil palm was responsible for only 32% of deforestation in Indonesia. If demand-side restrictions succeed in substantially reducing deforestation, it is likely to be through non-price pathways.