We present the first estimate of the Ly{alpha} luminosity function using blind spectroscopy from the Multi Unit Spectroscopic Explorer, MUSE, in the Hubble Deep Field-South. Using automatic source-detection software, we assemble a homogeneously detected sample of 59 Ly{alpha} emitters covering a flux range of -18.0<log_10_(F)<-16.3(erg/s/cm2), corresponding to luminosities of 41.4<log_10_(L)<42.8(erg/s). As recent studies have shown, Ly{alpha} fluxes can be underestimated by a factor of 2 or more via traditional methods, and so we undertake a careful assessment of each object's Ly{alpha} flux using a curve-of-growth analysis to account for extended emission. We describe our self-consistent method for determining the completeness of the sample, and present an estimate of the global Ly {alpha} luminosity function between redshifts 2.91<z<6.64 using the 1/V_max_ estimator. We find that the luminosity function is higher than many number densities reported in the literature by a factor of 2-3, although our result is consistent at the 1{sigma} level with most of these studies. Our observed luminosity function is also in good agreement with predictions from semi-analytic models, and shows no evidence for strong evolution between the high- and low-redshift halves of the data. We demonstrate that one's approach to Ly{alpha} flux estimation does alter the observed luminosity function, and caution that accurate flux assessments will be crucial in measurements of the faint-end slope. This is a pilot study for the Ly{alpha} luminosity function in the MUSE deep-fields, to be built on with data from the Hubble Ultra Deep Field that will increase the size of our sample by almost a factor of 10.