We investigate the photometric redshift accuracy achievable with the AKARI infrared data in deep multi-band surveys, such as in the North Ecliptic Pole field. We demonstrate that the passage of redshifted policyclic aromatic hydrocarbons and silicate features into the mid-infrared wavelength window covered by AKARI is a valuable means to recover the redshifts of starburst galaxies. To this end we have collected a sample of ~60 galaxies drawn from the GOODS-North Field with spectroscopic redshift 0.5<~z_spec<~1.5 and photometry from 3.6 to 24 micron, provided by the Spitzer, ISO and AKARI satellites. The infrared spectra are fitted using synthetic galaxy Spectral Energy Distributions which account for starburst and active nuclei emission. For ~90% of the sources in our sample the redshift is recovered with an accuracy |z_phot-z_spec|/(1+z_spec)<~10%. A similar analysis performed on different sets of simulated spectra shows that the AKARI infrared data alone can provide photometric redshifts accurate to |z_phot-z_spec|/(1+z_spec)<~10% (1-sigma) at z<~2. At higher redshifts the PAH features are shifted outside the wavelength range covered by AKARI and the photo-z estimates rely on the less prominent 1.6 micron stellar bump; the accuracy achievable in this case on (1+z) is ~10-15%, provided that the AGN contribution to the infrared emission is subdominant. Our technique is no more prone to redshift aliasing than optical-uv photo-z, and it may be possible to reduce this aliasing further with the addition of submillimetre and/or radio data.