Magnetic fields play important roles in star formation process in our Galaxy. On the other hand, the importance of the magnetic field on the star formation in the early universe has been recognized recently. However, before proceeding to the study on the dynamical effects of the magnetic field in such early star formation process, we have to understand the coupling between the magnetic field with the low metallicity gas, since it is the main ingredient of primordial galaxies. In this study, we explore the dissipation of the magnetic fields from the low metallicity gas clouds, utilizing the detailed chemical reaction model. As a result, we find that the magnetic field is alway frozen to the gas for Z<10-6Z⊙, while it could dissipate from the gas in the case of Z>10-6Z⊙ if the gas density falls within a certain range.