This is the second paper in our series about the search for multiple populations in Magellanic Cloud star clusters using the Hubble Space Telescope. Here we report the detection of multiple stellar populations in the colour-magnitude diagrams of the intermediate-age clusters Lindsay 1, NGC 416 and NGC 339. With ages between 6.0 and 7.5 Gyr, these clusters are the youngest ones in which chemical abundance spreads have been detected so far. This confirms that the appearance of multiple populations is not restricted to only ancient globular clusters, but may also be a common feature in clusters as young as 6 Gyr. Our results are in agreement with a recent spectroscopic study of Lindsay 1. We found that the fraction of enriched stars in NGC 416 is ~45 per cent whereas it is ~25 per cent in NGC 339 and ~36 per cent in Lindsay 1. Similar to NGC 121, these fractions are lower than the average value for globular clusters in the Milky Way.