We use Multi Unit Spectroscopic Explorer (MUSE) observations of the galaxy cluster MACSJ1149.5+2223 to explore the kinematics of the grand-design spiral galaxy (Sp1149) hostingthe supernova 'Refsdal'. Sp1149 lies at z ≃ 1.49, has a stellar mass M* ≃ 5 × 109Mo˙, hasa star formation rate (SFR) ≃ 1-6 Mo˙ yr-1, and represents a likely progenitor of a MilkyWay-like galaxy. All the four multiple images of Sp1149 in our data show strong [O II]-lineemissions pointing to a clear rotation pattern. We take advantage of the gravitational lensingmagnification effect (≈4×) on the [OII] emission of the least distorted image to fit threedimensionalkinematic models to the MUSE data cube and derive the rotation curve and thevelocity dispersion profile of Sp1149. We find that the rotation curve steeply rises, peaks atR ≈1 kpc, and then (initially) declines and flattens to an average Vflat = 128+29-19 km s-1. Theshape of the rotation curve is well determined, but the actual value of Vflat is quite uncertainbecause of the nearly face-on configuration of the galaxy. The intrinsic velocity dispersion dueto gas turbulence is almost constant across the entire disc with an average of 27 ± 5 kms-1.This value is consistent with z = 0 measurements in the ionized gas component and a factorof 2-4 lower than other estimates in different galaxies at similar redshifts. The average stellarto-total mass fraction is of the order of one-fifth. Our kinematic analysis returns the pictureof a regular star-forming, mildly turbulent, rotation-dominated (V/σ ≃ 5) spiral galaxy in a4-Gyr-old Universe.