We have examined dust emission in galaxy clusters at millimeter wavelengths using the Planck 857 GHz map to constrain the model based on Herschel observations that was used in studies for the Cosmic ORigins Explorer (CORE) mission concept. By stacking the emission from Planck-detected clusters, we estimated the normalization of the infrared luminosity versus mass relation and constrained the spatial profile of the dust emission. We used this newly constrained model to simulate clusters that we inject into Planck frequency maps. The comparison between clusters extracted using these gas+dust simulations and the basic gas-only simulations allows us to assess the impact of cluster dust emission on Planck results. In particular, we determined the impact on cluster parameter recovery (size, flux) and on Planck cluster cosmology results (survey completeness, determination of cosmological parameters). We show that dust emission has a negligible effect on the recovery of individual cluster parameters for the Planck mission, but that it impacts the cluster catalog completeness, reducing the number of detections in the redshift range [0.3–0.8] by up to ∼9%. Correcting for this incompleteness in the cosmological analysis has a negligible effect on cosmological parameter measurements: in particular, it does not ease the tension between Planck cluster and primary cosmic microwave background cosmologies.