We present a point-source detection algorithm that employs the second-order Spherical Mexican Hat wavelet filter (SMHW2), and use it on C-Band All-Sky Survey (C-BASS) northern intensity data to produce a catalogue of point sources. This catalogue allows us to cross-check the C-BASS flux-density scale against existing source surveys, and provides the basis for a source mask that will be used in subsequent C-BASS and cosmic microwave background (CMB) analyses. The SMHW2 allows us to filter the entire sky at once, avoiding complications from edge effects arising when filtering small sky patches. The algorithm is validated against a set of Monte Carlo simulations, consisting of diffuse emission, instrumental noise, and various point-source populations. The simulated source populations are successfully recovered. The SMHW2 detection algorithm is used to produce a $4.76\, \mathrm{GHz}$ northern sky source catalogue in total intensity, containing 1784 sources and covering declinations δ ≥ −10°. The C-BASS catalogue is matched with the Green Bank 6 cm (GB6) and Parkes-MIT-NRAO (PMN) catalogues over their areas of common sky coverage. From this we estimate the 90 per cent completeness level to be approximately $610\, \mathrm{mJy}$ , with a corresponding reliability of 98 per cent, when masking the brightest 30 per cent of the diffuse emission in the C-BASS northern sky map. We find the C-BASS and GB6 flux-density scales to be consistent with one another to within approximately 4 per cent.