Double bars make up a significant fraction of barred galaxies. We propose a new formation scenario for double bars that involves tidal interactions. We demonstrate the viability of this scenario using two examples of simulated galaxies from run TNG50-1 of the IllustrisTNG project. In the proposed scenario the inner bar forms first, either in isolation, via instabilities, or through previous tides. The outer bar forms later from the material that is tidally distorted by a strong interaction. The inner and outer bars formed this way rotate with different pattern speeds and can be mistaken for a single bar when their phases align. The double-barred structure is stable and can last for at least 3 Gyr. The inner bars of the tidally induced double bars can also have big sizes, which can possibly explain the origin of sizable inner bars recently found in some galaxies.