Aims. Observations with the Very Large Array telescope at 1477 MHz revealed the presence of a radio mini-halo surrounding the faint central point-like radio source in the Ophiuchus cluster of galaxies. In this work we present a study of the radio emission from this cluster of galaxies at lower radio frequencies. Methods. We observed the Ophiuchus cluster at 153, 240, and 614 MHz with the Giant Metrewave Radio Telescope. Results. The mini-halo is clearly detected at 153 and 240 MHz, the frequencies at which we reached the best sensitivity to the lowsurface brightness diffuse emission, while it is not detected at 610 MHz because of the too low signal-to-noise ratio at this frequency. The most prominent feature at low frequencies is a patch of diffuse steep spectrum emission located at about 5 south-east from the cluster centre. By combining these images with that at 1477 MHz, we derived the spectral index of the mini-halo. Globally, the minihalo has a low-frequency spectral index of α 153 240 1.4 ± 0.3 and an high-frequency spectral index of α 240 1477 1.60 ± 0.05. Moreover, we measure a systematic increase of the high-frequency spectral index with radius: the azimuthal radial average of α 240 1477 increases from about 1.3, at the cluster centre, up to about 2.0 in the mini-halo outskirts. Conclusions. The observed radio spectral index agrees with that obtained by modelling the non-thermal hard X-ray emission in this cluster of galaxies. We assume that the X-ray component arises from inverse-Compton scattering between the photons of the cosmic microwave background and a population of non-thermal electrons, which are isotropically distributed and whose energy spectrum is a power law with an index p. We derive that the electrons energy spectrum should extend from a minimum Lorentz factor of γ min 700 up to a maximum Lorentz factor of γ max 3.8 × 10 4 with an index p = 3.8 ± 0.4. The volume-averaged strength for a completely disordered intra-cluster magnetic field is B V 0.3 ± 0.1 μG.