SARS-CoV-2 mainly infects the respiratory tract but can also target other organs, including the central nervous system. While it was recently shown that cells of the blood-brain-barrier are permissive to SARS-CoV-2 infection in vitro, it remains debated whether neurons can be infected. In this study, we demonstrate that vesicular stomatitis virus particles pseudotyped with the spike protein of SARS-CoV-2 variants WT, Alpha, Delta and Omicron enter the neuronal model cell line SH-SY5Y. Cell biological analyses of the pseudo-virus treated cultures showed marked alterations in microtubules of SH-SY5Y cells. Because the changes in β-tubulin occurred in most cells, but only few were infected, we further asked whether interaction of the cells with spike protein might be sufficient to cause molecular and structural changes. For this, SH-SY5Y cells were incubated with trimeric spike proteins for time intervals of up to 24 h. CellProfiler™-based image analyses revealed changes in the intensities of microtubule staining in spike protein-incubated cells. Furthermore, expression of the spike protein-processing protease cathepsin L was found to be up-regulated by wild type, Alpha and Delta spike protein pseudotypes and cathepsin L was found to be secreted from spike protein-treated cells. We conclude that the mere interaction of the SARS-CoV-2 with neuronal cells can affect cellular architecture and proteolytic capacities. The molecular mechanisms underlying SARS-CoV-2 spike protein induced cytoskeletal changes in neuronal cells remain elusive and require future studies.