This paper derives highly accurate and effective closed-form formulas for the average upper bound on the pairwise error probability (PEP) of the multi-carrier index keying orthogonal frequency division multiplexing (MCIK-OFDM) system with low-complexity detection (i.e., greedy detection) in two-wave with diffuse power (TWDP) fading channels. To be specific, we utilize an exact moment generating function (MGF) of the signal-to-noise ratio (SNR) under TWDP fading to guarantee highly precise investigations of error probability performance; existing formulas for average PEP employ the approximate probability density function (PDF) of the SNR for TWDP fading, thereby inducing inherent approximation error. Moreover, some special cases of TWDP fading are also considered. To quantitatively reveal the achievable modulation gain and diversity order, we further derive asymptotic formulas for the upper bound on the average PEP. The obtained asymptotic expressions can be used to rapidly estimate the achievable error performance of MCIK-OFDM with the greedy detection over TWDP fading in high SNR regimes.