Sales of plant-based ‘meat’ and ‘milk’—products that mimic the visual and functional characteristics of animal-source foods—have increased rapidly during the past decade and are predicted to continue to increase. As plant-based ‘meat’ and ‘milk’ are nutritionally dissimilar to the animal-source originals, this study aimed to estimate the nutritional implications for the Australian population of substituting ‘Easily Swappable’ animal-source meat and dairy milk with plant-based imitation products. Computer simulation modelling was undertaken using dietary intake data collected in 2011–12 from a nationally representative survey sample. Conservative and Accelerated dietary transition scenarios were modelled in which various amounts of dairy milk and animal-source meat were replaced with plant-based ‘milk’ and plant-based ‘meat’, for the entire population and for various sub-populations. The scenarios were based on sales reports and economic projections. Modelling revealed that the intake of nutrients already at risk of inadequate intake, such as iodine and vitamin B12 (particularly for females), zinc (particularly for males) and n-3 long-chain fatty acids (for adults), would likely be adversely impacted in an Accelerated scenario. In conclusion, widespread replacement of dairy milk and animal-source meat with plant-based ‘milk’ and ‘meat’ may increase the risk of nutritional inadequacies in the Australian population. Messages and policy actions promoting the transition to more environmentally sustainable diets should be designed to avoid such adverse nutritional impacts.