Exoplanets of a few Earth masses can be now detected around nearby low-mass stars using Doppler spectroscopy. In this paper, we investigate the radial velocity variations of Kapteyn's star, which is both a sub-dwarf M-star and the nearest halo object to the Sun. The observations comprise archival and new HARPS, HIRES and PFS Doppler measurements. Two Doppler signals are detected at periods of 48 and 120 days using likelihood periodograms and a Bayesian analysis of the data. Using the same techniques, the activity indices and archival ASAS-3 photometry show evidence for low-level activity periodicities of the order of several hundred days. However, there are no significant correlations with the radial velocity variations on the same time-scales. The inclusion of planetary Keplerian signals in the model results in levels of correlated and excess white noise that are remarkably low compared to younger G, K and M dwarfs. We conclude that Kapteyn's star is most probably orbited by two super-Earth mass planets, one of which is orbiting in its circumstellar habitable zone, becoming the oldest potentially habitable planet known to date. The presence and long-term survival of a planetary system seems a remarkable feat given the peculiar origin and kinematic history of Kapteyn's star. The detection of super-Earth mass planets around halo stars provides important insights into planet-formation processes in the early days of the Milky Way.