Abstract: Einstenian cubic gravity (ECG) is a modified theory of gravity constructed with cubic contractions of the curvature tensor. This theory has the remarkable feature of having the same two propagating degrees of freedom of Einstein gravity (EG), at the perturbative level on maximally symmetric spacetimes. The additional unstable modes steaming from the higher order derivative dynamics are suppressed provided that we consider the ECG as an effective field theory wherein the cubic terms are seen as perturbative corrections of the Einstein -Hilbert term. Extensions of ECG have been proposed in cosmology and compact objects in order to probe if this property holds in more general configurations. In this work, we construct a modified ECG gravity in a five dimensional warped braneworld scenario. By assuming a specific combination of the cubic parameters, we obtained modified gravity equations of motion with terms up to second -order. For a thin 3-brane, the cubic -gravity corrections yield an effective positive bulk cosmological constant. Thus, in order to keep the 5D bulk warped compact, an upper bound of the cubic parameter with respect to the bulk curvature was imposed. For a thick brane, the cubic -gravity terms modify the scalar field potential and its corresponding vacuum. Nonetheless, the domain -wall structure with a localized source is preserved. At the perturbative level, the Kaluza-Klein (KK) tensor gravitational modes are stable and possess a localized massless mode provided the cubic corrections are small compared to the EG braneworld.