Abstract Imaging atmospheric Cherenkov telescopes (IACTs) are ground-based indirect detectors for cosmic gamma rays with energies above tens of GeV. The major backgrounds for gamma-ray observations in IACTs are cosmic-ray charged particles. The capability to reject these backgrounds is the most important factor determining the gamma-ray sensitivity of IACT systems. Monte Carlo simulations are used to estimate the residual background rates and sensitivity of the systems during the design and construction phase. Uncertainties in the modeling of high-energy hadronic interactions of cosmic rays with nuclei in the air propagate into the estimates of residual background rates and subsequently into the estimated instrument sensitivity. We investigate the influence of the difference in the current hadronic interaction models on the estimated gamma-ray sensitivity of the Cherenkov Telescope Array using four interaction models (QGSJET-II-03, QGSJET-II-04, EPOS-LHC, and SIBYLL2.3c) implemented in the air shower simulation tool CORSIKA. Variations in background rates of up to a factor 2 with respect to QGSJET-II-03 are observed between the models, mainly due to differences in the π 0 production spectrum. These lead to ∼30% differences in the estimated gamma-ray sensitivity in the 1–30 TeV region, assuming a 50 h observation of a gamma-ray point-like source. The presented results also show that IACTs have a significant capability in the verification of hadronic interaction models.