The electrically tunable properties of liquid-crystal fishnet metamaterials are theoretically investigated in the terahertz spectrum. A nematic liquid crystal layer is introduced between two fishnet metallic structures, forming a voltage-controlled metamaterial cavity. Tuning of the nematic molecular orientation is shown to shift the magnetic resonance frequency of the metamaterial and its overall electromagnetic response. A shift higher than 150 GHz is predicted for common dielectric and liquid crystalline materials used in terahertz technology and for low applied voltage values. Owing to the few micron-thick liquid crystal cell, the response speed of the tunable metamaterial is calculated as orders of magnitude faster than in demonstrated liquid-crystal based non-resonant terahertz components. Such tunable metamaterial elements are proposed for the advanced control of electromagnetic wave propagation in terahertz applications.