We present a robust, efficient, and user-friendly algorithm for detecting faint emission-line sources in large integral-field spectroscopic datacubes together with the public release of the software package Line Source Detection and Cataloguing (LSDCat). LSDCat uses a three-dimensional matched filter approach, combined with thresholding in signal-to-noise, to build a catalogue of individual line detections. In a second pass, the detected lines are grouped into distinct objects, and positions, spatial extents, and fluxes of the detected lines are determined. LSDCat requires only a small number of input parameters, and we provide guidelines for choosing appropriate values. The software is coded in Python and capable of processing very large datacubes in a short time. We verify the implementation with a source insertion and recovery experiment utilising a real datacube taken with the MUSE instrument at the ESO Very Large Telescope.