In this paper, we propose a novel method for a robot to detect robot-directed speech, that is, to distinguish speech that users speak to a robot from speech that users speak to other people or to themselves. The originality of this work is the introduction of a multimodal semantic confidence (MSC) measure, which is used for domain classification of input speech based on the decision on whether the speech can be interpreted as a feasible action under the current physical situation in an object manipulation task. This measure is calculated by integrating speech, object, and motion confidence with weightings that are optimized by logistic regression. Then we integrate this measure with gaze tracking and conduct experiments under conditions of natural human-robot interaction. Experimental results show that the proposed method achieves a high performance of 94% and 96% in average recall and precision rates, respectively, for robot-directed speech detection.