Context. Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT and Kepler space missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect. Aims. Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed by Kepler and have therefore been extensively observed, with exquisite precision on their oscillation frequencies. Methods. We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form. Results. We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is 320 ± 269 nHz and 440₋₃₈₃⁺³⁶³ nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are 535 ± 75 nHz and 565₋₁₂₉⁺¹⁵⁰ nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry. Conclusions. We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters.