Provided is a control apparatus for an internal combustion engine that can suppress blowback of in-cylinder residual gas to an intake passage when reverting from a fuel-cut operation accompanied by valve stopping control of an intake valve while suppressing an oil ascent during execution of the fuel-cut operation, and a control apparatus for a vehicle equipped with the internal combustion engine. When executing a fuel-cut operation accompanied by intake valve stopping control, advancement control of the opening/closing timing of an exhaust valve (32) is executed. If the advancement control is being executed in a case where a request to revert from the fuel-cut operation has been detected, an advance amount of the opening/closing timing of the exhaust valve (32) is retarded so as to become less than or equal to a predetermined value.