The influence of in-phase and quadrature (IQ) imbalance on the performance of orthogonal time frequency space (OTFS) transmission is investigated in this work. OTFS is a recent two-dimensional transmission scheme with promising robustness against the time and frequency selectivity of the time-varying wireless channel, and IQ impairment arises from inevitable imperfections between in-phase and quadrature branches in the transceiver design. In this paper, the mathematical model is presented to illustrate the physical effect of the IQ mismatched transmitter in OTFS, which results in a new type of interference named mirror-Doppler interference (MDI), occurring only along the Doppler axis. Moreover, a closed-form expression for the average bit error rate (BER) of OTFS with IQ imbalanced transmitter is derived taking into account M-ary symbol with a constant envelope and maximum likelihood (ML) detection principle. Importantly, our findings prove that IQ imbalanced transmitter causes a significant reduction in the diversity gain of OTFS transmission, but does not lead to an error floor in the BER performance as in one-dimensional current communication systems. Monte-Carlo simulations are provided to validate the derived mathematical formulas for OTFS transmission with constant envelope M-ary symbols under different system configurations.