We present results of a search for the 3.5 keV emission line in our recent very long (similar to 1.4 Ms) XMM-Newton observation of the Draco dwarf spheroidal galaxy. The astrophysical X-ray emission from such dark matter-dominated galaxies is faint, thus they provide a test for the dark matter origin of the 3.5 keV line previously detected in other massive, but X-ray bright objects, such as galaxies and galaxy clusters. We do not detect a statistically significant emission line from Draco; this constrains the lifetime of a decaying dark matter particle to tau > (7-9) x 10(27) s at 95 per cent CL (combining all three XMM-Newton cameras; the interval corresponds to the uncertainty of the dark matter column density in the direction of Draco). The PN camera, which has the highest sensitivity of the three, does show a positive spectral residual (above the carefully modelled continuum) at E = 3.54 +/- A 0.06 keV with a 2.3 sigma significance. The two MOS cameras show less-significant or no positive deviations, consistently within 1 sigma with PN. Our Draco limit on tau is consistent with previous detections in the stacked galaxy clusters, M31 and the Galactic Centre within their 1 - 2 sigma uncertainties, but is inconsistent with the high signal from the core of the Perseus cluster (which has itself been inconsistent with the rest of the detections). We conclude that this Draco observation does not exclude the dark matter interpretation of the 3.5 keV line in those objects.