We present the first measurement of the fluctuations in the number of muons in inclined air showers with energies above 4 EeV measured with the Pierre Auger Observatory. We find that the results agree well with simulations within the experimental uncertainties. In contrast, the measurement of the average number of muons has previously been found to deviate substantially from the prediction by high-energy hadronic interaction models. We analyse the implications of these findings for our understanding of hadronic interactions, especially to those at the highest energies.