The recent introduction of Zika virus (ZIKV), the recurrence of dengue virus (DENV), and the lethality of yellow fever virus (YFV) have had a significant impact on Brazilian society and public health. Here, we targeted two cellular kinases implicated in cell proliferation and cancer that are also important for viral replication: mitogen-activated protein kinase kinase (MEK) and Src. We used two MEK inhibitors - trametinib and selumetinib - and two Src inhibitors - saracatinib and bosutinib - to inhibit ZIKV, DENV, and YFV replication in cell culture. The cytotoxicity of the four inhibitors was determined by the observation of abnormal morphology and quantification of adherent cells by crystal violet staining. The antiviral activity of these drugs was assessed based on the reduction of plaque-forming units in cell culture as evidence of the inhibition of the replication of the selected flaviviruses. All four inhibitors showed antiviral activity, but among them, trametinib was the safest and most efficacious against all of the viruses, inhibiting the replication of ZIKV and YFV by 1000-fold, and DENV2/3 by nearly 100-fold. This pan-antiviral effect shows that trametinib could be repurposed for the treatment of flaviviral infections.