Most climate projections represent volcanic eruptions as a prescribed constant forcing based on a historical average, which prevents a full quantification of uncertainties in climate projections. Here we show that the contribution of volcanic forcing uncertainty to the overall uncertainty in global mean surface air temperature projections reaches up to 49% in 2029, and is comparable or greater than that from internal variability throughout the 21st century. Furthermore, compared to a constant volcanic forcing, employing a stochastic volcanic forcing reduces the probability of exceeding 1.5 °C warming above pre-industrial level by at least 5% for high climate mitigation scenario, and enhances the probability of negative decadal temperature trends by up to 8%. Intermediate to high climate mitigation scenarios are particularly sensitive to the choice of future volcanic forcing implementation. We recommend the use of either a stochastic approach or prescribed constant forcing levels that sample volcanic uncertainty in future climate simulations.