An apparatus and method for controlling a clutch of a hybrid vehicle are provided. The method includes: setting, by a controller, a limited torque to a motor torque and comparing an input speed of the transmission and a minimum speed of the engine when converting from an EV driving mode to an HEV driving mode. The controller is configured to start the engine when the input speed of the transmission is equal to or greater than a minimum threshold point and is equal to or less than a minimum speed of the engine. Further, the method includes increasing the motor torque to exceed the preset limited torque, coupling the first clutch when the engine speed and a motor speed are synchronized, and coupling the second clutch when the input speed of the transmission exceeds the minimum speed of the engine by the controller.