As AI technologies progress, social acceptance of AI agents, including intelligent virtual agents and robots, is becoming even more important for more applications of AI in human society. One way to improve the relationship between humans and anthropomorphic agents is to have humans empathize with the agents. By empathizing, humans act positively and kindly toward agents, which makes it easier for them to accept the agents. In this study, we focus on self-disclosure from agents to humans in order to increase empathy felt by humans toward anthropomorphic agents. We experimentally investigate the possibility that self-disclosure from an agent facilitates human empathy. We formulate hypotheses and experimentally analyze and discuss the conditions in which humans have more empathy toward agents. Experiments were conducted with a three-way mixed plan, and the factors were the agents’ appearance (human, robot), self-disclosure (high-relevance self-disclosure, low-relevance self-disclosure, no self-disclosure), and empathy before/after a video stimulus. An analysis of variance (ANOVA) was performed using data from 918 participants. We found that the appearance factor did not have a main effect, and self-disclosure that was highly relevant to the scenario used facilitated more human empathy with a statistically significant difference. We also found that no self-disclosure suppressed empathy. These results support our hypotheses. This study reveals that self-disclosure represents an important characteristic of anthropomorphic agents which helps humans to accept them.