Context. One of the major science cases of the Multi Unit Spectroscopic Explorer (MUSE) integral field spectrograph is the detection of Lyman-alpha emitters at high redshifts. The on-going and planned deep fields observations will allow for one large sample of these sources. An efficient tool to perform blind detection of faint emitters in MUSE datacubes is a prerequisite of such an endeavor.Aims. Several line detection algorithms exist but their performance during the deepest MUSE exposures is hard to quantify, in particular with respect to their actual false detection rate, or purity. The aim of this work is to design and validate an algorithm that efficiently detects faint spatial-spectral emission signatures, while allowing for a stable false detection rate over the data cube and providing in the same time an automated and reliable estimation of the purity.Methods. The algorithm implements (i) a nuisance removal part based on a continuum subtraction combining a discrete cosine transform and an iterative principal component analysis, (ii) a detection part based on the local maxima of generalized likelihood ratio test statistics obtained for a set of spatial-spectral profiles of emission line emitters and (iii) a purity estimation part, where the proportion of true emission lines is estimated from the data itself: the distribution of the local maxima in the “noise only” configuration is estimated from that of the local minima.Results. Results on simulated data cubes providing ground truth show that the method reaches its aims in terms of purity and completeness. When applied to the deep 30 h exposure MUSE datacube in the Hubble Ultra Deep Field, the algorithms allows for the confirmed detection of 133 intermediate redshifts galaxies and 248 Lyα emitters, including 86 sources with no Hubble Space Telescope counterpart.Conclusions. The algorithm fulfills its aims in terms of detection power and reliability. It is consequently implemented as a Python package whose code and documentation are available on GitHub and readthedocs.