This letter studies the equalizer design for orthogonal time-frequency space modulation (OTFS) under an impulsive noise (IN) environment with known IN statistics. To this end, a low complexity expectation propagation (EP) based joint equalization and IN mitigation approach for OTFS is proposed. Specifically, the posterior probability is decomposed into four factors: IN prior, demapper, discrete Zak transform (DZT) hard constraint, and channel factor. Approximating each factor as Gaussian with structured covariance according to the iterative EP update rules, the data symbols and IN can be jointly equalized and mitigated in the time-domain by efficiently exploiting the quasi-banded nature of the channel matrix. Finally, bit-error-rate (BER) results demonstrate the superiority of our proposed approach over the existing EP-based OTFS equalizer under impulsive noise impairment.