Emerging viruses pose an important global public health challenge, and early action is needed to control their spread. The Bunyaviridae family contains a great number of arboviruses which are potentially pathogenic for humans. For example, phleboviruses affect a large range of hosts, including humans and animals. Some infections usually have an asymptomatic course, but others lead to severe complications, such as Toscana virus, which is able to cause meningitis and encephalitis. Unfortunately, to date, no vaccines or antiviral treatments have been found. In the present study, we evaluated the effect of melittin-related peptides, namely the frog-derived RV-23 and AR-23, on sandfly fever Naples virus infection in vitro. Both peptides exhibited a strong antiviral activity by targeting the viral particles and blocking the virus–cell interaction. Their action was directed to an early phase of SFNV infection, in particular at viral adsorption on host cells, by interfering with the binding of common glycosaminoglycan receptors. Given the better antimicrobial behavior of AR-23 and RV-23 compared to melittin in terms of selectivity, our studies expand our understanding of the potential of these peptides as antimicrobials and stimulate further investigations in the direction of novel antiviral strategies against phlebovirus infection.