We consider a molecular communication system comprised of a transmitter, an absorbing receiver, and an interference source. Assuming amplitude modulation, we analyze the dependence of the bit error rate (BER) on the detection interval, which is the time within one transmission symbol interval during which the receiver is active to absorb and detect the number of information-carrying molecules. We then propose efficient algorithms to determine the optimal detection interval that minimizes the BER of the molecular communication system assuming no inter-symbol interference (ISI). Simulation and numerical evaluations are provided to highlight further insights into the optimal results. For example, we demonstrate that the optimal detection interval can be very small compared to the transmission symbol interval. Moreover, our numerical results show that significant BER improvements are achieved by using the optimal detection interval for systems without and with ISI.