We present a catalogue of about six million unresolved photometric detections in the Sloan Digital Sky Survey (SDSS) Seventh Data Release, classifying them into stars, galaxies and quasars. We use a machine learning classifier trained on a subset of spectroscopically confirmed objects from 14th to 22nd magnitude in the SDSS i band. Our catalogue consists of 2430625 quasars, 3544036 stars and 63586 unresolved galaxies from 14th to 24th magnitude in the SDSS i-band. Our algorithm recovers 99.96 per cent of spectroscopically confirmed quasars and 99.51 per cent of stars to i~21.3 in the colour window that we study. The level of contamination due to data artefacts for objects beyond i=21.3 is highly uncertain and all mention of completeness and contamination in the paper are valid only for objects brighter than this magnitude. However, a comparison of the predicted number of quasars with the theoretical number counts shows reasonable agreement.