In this work, we propose a low-overhead channel estimator for diffusive molecular communication systems. Since diffusive molecular communication systems rely on the random propagation of molecules as a means of communication, they may potentially suffer from inter-symbol-interference in addition to the noise introduced by the channel and external sources. Hence, acquiring an accurate estimate of the channel impulse response is essential for signal equalization and detection. The proposed low-overhead estimator utilizes a minimal number of pilot symbols, thus reducing the training overhead by up to 95%. The computational complexity of the proposed estimator is comparable to that of pilot-based least-squared estimators in related works. Consequently, the proposed low-overhead channel estimator is efficient in terms of throughput and complexity in a way that appeals to the majority of prospective diffusive molecular communication systems.