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To push the radial velocity (RV) exoplanet detection threshold, it is crucial to find more reliable radial velocity extraction methods. The Least-Squares Deconvolution (LSD) technique has been used to infer the stellar magnetic flux from spectropolarimetric data for the past two decades. It relies on the assumption that stellar absorption lines are similar in shape. Although this assumption is simplistic, LSD provides a good model for intensity spectra and likewise an estimate for their Doppler shift. We present the Multi-Mask Least-Squares Deconvolution (MM-LSD) RV extraction pipeline which extracts the radial velocity from two-dimensional echelle-order spectra using LSD with multiple tailored masks after continuum normalisation and telluric absorption line correction. The flexibility of LSD allows to exclude spectral lines or pixels at will, providing a means to exclude variable lines or pixels affected by instrumental problems. The MM-LSD pipeline was tested on HARPS-N data for the Sun and selected well-observed stars with 5.7 < Vmag < 12.6. For FGK-type stars with median signal-to-noise above 100, the pipeline delivered RV time series with on average 12 per cent lower scatter as compared to the HARPS-N RV extraction pipeline based on the Cross-Correlation Function technique. The MM-LSD pipeline may be used as a standalone RV code, or modified and extended to extract a proxy for the magnetic field strength.