The Zika virus (ZIKV) is a great concern for global health due to its high transmission, including disseminating through blood, saliva, urine, semen and vertical transmission. In some cases, ZIKV has been associated with microcephaly, neurological disorders, and Guillain–Barré syndrome. There is no vaccine, and controlling the disease is a challenge, especially with the co-circulation of the Dengue virus, which causes a severe cross-reaction due to the similarity between the two arboviruses. Considering that electrochemical immunosensors are well-established, sensitive, and practical tools for diagnosis, in this study we developed a sensor platform with intrinsic redox activity that facilitates measurement readouts. Prussian blue (PB) has a great ability to form electrocatalytic surfaces, dispensing redox probe solutions in voltammetric measurements. Herein, PB was incorporated into a chitosan–carbon nanotube hybrid, forming a nanocomposite that was drop-casted on a screen-printed electrode (SPE). The immunosensor detected the envelope protein of ZIKV in a linear range of 0.25 to 1.75 µg/mL (n = 8, p < 0.01), with a 0.20 µg/mL limit of detection. The developed immunosensor represents a new method for electrochemical measurements without additional redox probe solutions, and it is feasible for application in point-of-care diagnosis.