Recent numerical calculations have shown that while strong toroidal rotation can increase the external kink limit of tokamak plasmas, the associated rotation shear can drive a Kelvin-Helmholtz like global instability in the plasma, if the rotation frequency exceeds a threshold value (Chapman et al 2011 Plasma Phys. Control. Fusion 53 125002; Chapman et al 2012 Nucl. Fusion 52 042005). On the basis of a large aspect ratio toroidal expansion of the magnetohydrodynamic stability equations, the present paper investigates analytically various properties of this instability in tokamak plasmas with sonic toroidal flows and low magnetic shear in the core region. We also compare the analytical results with numerical code calculations. Many characteristic features and parameter dependences of the instability can be understood from the analytical theory, such as an eigenmode structure peaking at the position of largest rotation shear, and insensitivity of the growth rate to the plasma beta and to the precise value of the safety factor in the region of low magnetic shear. From an algebraic expression for the growth rate, valid asymptotically at large rotation frequencies, the drop in the dynamic pressure associated with the flow in the plasma can be identified as a major driving mechanism of the instability. For modes with (dominant) poloidal mode number m > 1, and rotating equilibria with isothermal magnetic surfaces, another driving mechanism of the instability is related to the centrifugally induced density variation along the magnetic field lines.