Auxetic materials are characterized by a negative Poisson's ratio that they expand laterally in the directions perpendicular to the applied stretching stress and vice versa. Piezoelectrics will change their dimensions when exposed to an external electric field. Here we introduce the concept of the "electric auxetic effect": electric auxetic materials will contract or expand in all dimensions in response to an electric field. Such unusual piezoelectric response driven by an electric field is a close analogy to the auxetic effect driven by a stress field. A key feature of electric auxetic materials is that their longitudinal and transverse piezoelectric coefficients are of the same sign. We demonstrate using first-principles calculations that the Pca2_{1} orthorhombic phase of ferroelectric HfO_{2} exhibits both the negative longitudinal piezoelectric effect and the electric auxetic effect. The unusual negative longitudinal piezoelectric effect arises unexpectedly from the domination of the negative internal-strain contribution over the positive clamped-ion contribution, a character often found in van der Waals solids. We confirm a few more electric auxetic materials with finite electric field calculations by screening through a first-principles-based database of piezoelectrics.