During an X-ray survey of the Small Magellanic Cloud, carried out with the XMM-Newton satellite, we detected significant soft X-ray emission from the central star of the high-excitation planetary nebula SMP SMC 22. Its very soft spectrum is reproduced well with a non-local thermodynamical equilibrium model atmosphere composed of H, He, C, N, and O, with abundances equal to those inferred from studies of its nebular lines. The derived effective temperature of 1.5 × 10 5 K is in close agreement with that found from the optical/UV data. The unabsorbed flux in the 0.1-0.5 keV range is ∼3 × 10 −11 erg cm −2 s −1 , corresponding to a luminosity of ∼1.2 × 10 37 erg s −1 at a distance of 60 kpc. We also searched for X-ray emission from a large number of SMC planetary nebulae, confirming the previous detection of SMP SMC 25 with a luminosity of (0.2−6) × 10 35 erg s −1 (0.1-1 keV). For the remaining objects that were not detected, we derived flux upper limits corresponding to luminosity values from several tens to hundreds times lower than that of SMP SMC 22. The exceptionally high X-ray luminosity of SMP SMC 22 is probably due to the high mass of its central star, which is rapidly evolving toward the white dwarf's cooling branch, and to a small amount of intrinsic absorption in the nebula itself.