A fuel injector is disclosed for use in an engine system. The fuel injector may have a body defining a gas inlet, an oil inlet, and an oil outlet. The fuel injector may also have a nozzle connected to the body and having a base end in fluid communication with the gas inlet, and an injection tip located opposite the base end. The fuel injector may also have a valve check disposed in the nozzle and movable to selectively block and unblock the injection tip of the nozzle, and a plunger disposed in the body between the oil inlet and the oil outlet. The plunger may be movable between a flow-passing position and a flow-blocking position to cause movement of the valve check through the injection tip. The injector may further have a solenoid actuator configured to selectively move the plunger.