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Malware attacks have become very common in recent years. The variety and continuous improvement of malware capabilities threaten any network. Wi-Fi is also not an exception in that context. This paper proposes a model describing the spreading of malware in Wi-Fi networks using an epidemiological mathematical model. This model is built on the characteristics of encryption and authentication in Wi-Fi networks. In addition, we also consider state transitions of devices based on some assumptions about modern malware capabilities. We calculate the basic reproduction number <inline-formula> <tex-math notation="LaTeX">$\boldsymbol {R}_{0}$ </tex-math></inline-formula> and thereby indicate the condition to limit the spread of malware. This spreading model is analyzed through numerical simulation. Besides, for the readers to have an overview of the main threats and the security capabilities of the Wi-Fi devices, we also briefly present security threats and encryption methods used in Wi-Fi.