The effect of toroidal rotation on the ideal magnetohydrodynamic stability of the internal kink, or quasi-interchange, mode in tokamak plasmas with the safety factor, q, close to unity within a wide region in the plasma core is analysed. For equilibria with a large aspect ratio and circular cross section it is shown that rigid, toroidal rotation stabilizes the quasi-interchange mode if the rotation frequency, Ω, exceeds a critical frequency, Ωcrit, and a simple expression for Ωcrit is derived. Unless the plasma pressure and the radial extent of the low-shear region are both rather large, rotation frequencies of the order of a few per cent of the Alfvén frequency are found to be sufficient to stabilize the quasi-interchange mode. The stabilization is caused by the nonuniform plasma density and the associated Brunt–Väisälä (BV) frequency created by the centrifugal force. When Ω exceeds Ωcrit, the quasi-interchange instability transforms into a stable oscillation with a frequency close to the lowest BV-frequency in the low-shear region of the plasma.