Magnetic detection electrical impedance tomography (MDEIT) is an imaging modality that aims to reconstruct the cross-sectional conductivity distribution of a volume from the magnetic flux density surrounding an object. The MDEIT inverse problem is inherently ill-posed, necessitating the use of regularization. The most commonly used L2 norm regularizations generate the minimum energy solution, which blurs the sharp variations of the reconstructed image. Consequently, this paper presents the total variation (TV) regularization to preserve discontinuities and piecewise constancy of the MDEIT reconstructed image. The primal dual-interior point method (PD-IPM) is employed for minimizing the TV penalty in this paper. The proposed method is validated by MDEIT simulated data. In comparison with the performance of L2 norm regularization, the results show that TV regularized algorithm produces sharper images and has better robustness to noise. The TV regularized algorithm preserves local smoothness and piecewise constancy, leading to improvements in the localization of the reconstructed conductivity images in MDEIT.