Adaptation of zoonotic influenza viruses towards efficient human-to-human transmissibility is a substantial public health concern. The recently emerged A/H7N9 influenza viruses in China provide an opportunity for quantitative studies of host-adaptation, as human-adaptive substitutions in the PB2 gene of the virus have been found in all sequenced human strains, while these substitutions have not been detected in any non-human A/H7N9 sequences. Given the currently available information, this observation suggests that the human-adaptive PB2 substitution might confer a fitness advantage to the virus in these human hosts that allows it to rise to proportions detectable by consensus sequencing over the course of a single human infection. We use a mathematical model of within-host virus evolution to estimate the fitness advantage required for a substitution to reach predominance in a single infection as a function of the duration of infection and the fraction of mutant present in the virus population that initially infects a human. The modeling results provide an estimate of the lower bound for the fitness advantage of this adaptive substitution in the currently sequenced A/H7N9 viruses. This framework can be more generally used to quantitatively estimate fitness advantages of adaptive substitutions based on the within-host prevalence of mutations. Such estimates are critical for models of cross-species transmission and host-adaptation of influenza virus infections.