We present photometry of the nearby galaxy NGC 5128 (Centaurus A) observed with the Photodetector Array Camera and Spectrometer (PACS) and Spectral and Photometric Imaging Receiver (SPIRE) instruments on board the Herschel Space Observatory, at 70, 160, 250, 350 and 500 μm, as well as new CO J= 3–2 observations taken with the HARP-B instrument on the James Clerk Maxwell Telescope (JCMT). Using a single-component modified blackbody, we model the dust spectral energy distribution within the disc of the galaxy using all five Herschel wavebands and find dust temperatures of ∼30 K towards the centre of the disc and a smoothly decreasing trend to ∼20 K with increasing radius. We find a total dust mass of (1.59 ± 0.05) × 107 M⊙ and a total gas mass of (2.7 ± 0.2) × 109 M⊙. The average gas-to-dust mass ratio is 103 ± 8, but we find an interesting increase in this ratio to approximately 275 towards the centre of Cen A. We discuss several possible physical processes that may be causing this effect, including dust sputtering, jet entrainment and systematic variables such as the XCO factor. Dust sputtering by X-rays originating in the active galactic nucleus or the removal of dust by the jets is our most favoured explanation.