The COVID-19 pandemic, caused by the worldwide spread of SARS-CoV-2, has prompted the scientific community to rapidly develop efficient and specific diagnostics and therapeutics. A number of avenues have been explored, including the manufacture of COVID-related proteins to be used as reagents for diagnostics or treatment. The production of RBD and Spike proteins was previously achieved in eukaryotic cells, mainly mammalian cell cultures, while the production in microbial systems has been unsuccessful until now. Here we report the effective production of SARS-CoV-2 proteins in two plant model systems. We established transgenic tobacco BY-2 and Medicago truncatula A17 cell suspension cultures stably producing the full-length Spike and RBD recombinant proteins. For both proteins, various glycoforms were obtained, with higher yields in Medicago cultures than BY-2. This work highlights that RBD and Spike can be secreted into the culture medium, which will impact subsequent purification and downstream processing costs. Analysis of the culture media indicated the presence of the high molecular weight Spike protein of SARS-CoV-2. Although the production yields still need improvement to compete with mammalian systems, this is the first report showing that plant cell suspension cultures are able to produce the high molecular weight Spike protein. This finding strengthens the potential of plant cell cultures as production platforms for large complex proteins.