Measurement-induced transmon ionization refers to the phenomenon where the quantum nondemolition (QND) character of dispersive qubit readout in circuit quantum electrodynamics (circuit QED) is compromised due to measurement-induced transitions to highly excited states of the transmon. This process is analyzed using three complementary models: a fully quantized transmon-resonator model, a semiclassical model treating the resonator as a classical drive, and a fully classical model. All three models predict similar results, showing that transmon ionization occurs at specific resonator photon numbers, which are in agreement with experimental observations. The transmon's negative anharmonicity and the qubit-resonator frequency detuning play crucial roles in this process. At negative detuning (qubit frequency below resonator frequency), transmon states near the top of the cosine potential well are more susceptible to ionization, while at positive detuning (qubit frequency above resonator frequency), the opposite is true. The critical photon number for ionization depends on the gate charge, which influences the charge dispersion of the transmon states. The critical photon number is defined as the minimum photon number at which the average transmon population reaches a threshold value (N_t = 2 for the ground-state branch and N_t = 3 for the excited-state branch). The analysis reveals that multiphoton resonances are responsible for transmon ionization, and that the dispersive approximation breaks down at specific photon numbers. The results show that the ionization threshold is significantly affected by the gate charge, highlighting the importance of preserving the full cosine potential of the transmon in theoretical models. The findings provide a comprehensive framework for understanding and predicting transmon ionization in circuit QED experiments.Measurement-induced transmon ionization refers to the phenomenon where the quantum nondemolition (QND) character of dispersive qubit readout in circuit quantum electrodynamics (circuit QED) is compromised due to measurement-induced transitions to highly excited states of the transmon. This process is analyzed using three complementary models: a fully quantized transmon-resonator model, a semiclassical model treating the resonator as a classical drive, and a fully classical model. All three models predict similar results, showing that transmon ionization occurs at specific resonator photon numbers, which are in agreement with experimental observations. The transmon's negative anharmonicity and the qubit-resonator frequency detuning play crucial roles in this process. At negative detuning (qubit frequency below resonator frequency), transmon states near the top of the cosine potential well are more susceptible to ionization, while at positive detuning (qubit frequency above resonator frequency), the opposite is true. The critical photon number for ionization depends on the gate charge, which influences the charge dispersion of the transmon states. The critical photon number is defined as the minimum photon number at which the average transmon population reaches a threshold value (N_t = 2 for the ground-state branch and N_t = 3 for the excited-state branch). The analysis reveals that multiphoton resonances are responsible for transmon ionization, and that the dispersive approximation breaks down at specific photon numbers. The results show that the ionization threshold is significantly affected by the gate charge, highlighting the importance of preserving the full cosine potential of the transmon in theoretical models. The findings provide a comprehensive framework for understanding and predicting transmon ionization in circuit QED experiments.