Orthogonal Time Frequency Space (OTFS) has been proven to have strong robustness to Doppler shifts and is regarded as a potential candidate for Orthogonal Frequency Division Multiplexing (OFDM) in the next generation wireless communication. However, narrowband interference (NBI) may become a headache for OTFS-based wireless systems. In OTFS, NBI will be spread over the whole delay-Doppler (DD) domain, and thus cause serious interference. Such interference is very dangerous in OTFS-based high-mobility communication for it will let the fast-moving user equipment (UE) in danger of losing control. Previous work infers OTFS to have natural robustness to NBI. In this work, we conduct further analysis and come to the conclusion that such robustness is only capable when NBI is weak, but when NBI gets stronger, OTFS exhibits vulnerability to it. Then we propose an NBI suppression scheme for OTFS to detect and eliminate NBI with a low computation load. Simulation results prove our analysis and indicate the proposed scheme can prevent serious interference resulting from NBI to some extent.