SARS-CoV-2 is currently causing an unprecedented pandemic. While vaccines are massively deployed, we still lack effective large-scale antiviral therapies. In the quest for antivirals targeting conserved structures, we focused on molecules able to bind viral RNA secondary structures. Aminoglycosides are a class of antibiotics known to interact with the ribosomal RNA of both prokaryotes and eukaryotes and have previously been shown to exert antiviral activities by interacting with viral RNA. Here we show that the aminoglycoside geneticin is endowed with antiviral activity against all tested variants of SARS-CoV-2, in different cell lines and in a respiratory tissue model at non-toxic concentrations. The mechanism of action is an early inhibition of RNA replication and protein expression related to a decrease in the efficiency of the -1 programmed ribosomal frameshift (PRF) signal of SARS-CoV-2. Using in silico modeling, we have identified a potential binding site of geneticin in the pseudoknot of frameshift RNA motif. Moreover, we have selected, through virtual screening, additional RNA binding compounds, interacting with the same site with increased potency.