We present the results of a search for transversely polarised hidden photons (HPs) with ~ 3 eV energies emitted from the Sun. These hypothetical particles, known also as paraphotons or dark sector photons, are theoretically well motivated for example by string theory inspired extensions of the Standard Model. Solar HPs of sub-eV mass can convert into photons of the same energy (photon ↔ HP oscillations are similar to neutrino flavour oscillations). At SHIPS this would take place inside a long light-tight high-vacuum tube, which tracks the Sun. The generated photons would then be focused into a low-noise photomultiplier at the far end of the tube. Our analysis of 330 h of data (and 330 h of background characterisation) reveals no signal of photons from solar hidden photon conversion. We estimate the rate of newly generated photons due to this conversion to be smaller than 25 mHz/m2 at the 95% C.L . Using this and a recent model of solar HP emission, we set stringent constraints on χ, the coupling constant between HPs and photons, as a function of the HP mass.