Flaviviruses are arthropod-borne RNA viruses found worldwide that, when introduced into the human body, cause diseases, including neuroinfections, that can lead to serious metabolic consequences and even death. Some of the diseases caused by flaviviruses occur continuously in certain regions, while others occur intermittently or sporadically, causing epidemics. Some of the most common flaviviruses are West Nile virus, dengue virus, tick-borne encephalitis virus, Zika virus and Japanese encephalitis virus. Since all the above-mentioned viruses are capable of penetrating the blood–brain barrier through different mechanisms, their actions also affect the central nervous system (CNS). Like other viruses, flaviviruses, after entering the human body, contribute to redox imbalance and, consequently, to oxidative stress, which promotes inflammation in skin cells, in the blood and in CNS. This review focuses on discussing the effects of oxidative stress and inflammation resulting from pathogen invasion on the metabolic antiviral response of the host, and the ability of viruses to evade the consequences of metabolic changes or exploit them for increased replication and further progression of infection, which affects the development of sequelae and difficulties in therapy.