Cooperation between humans and machines is increasingly vital as artificial intelligence (AI) becomes more integrated into daily life. Research indicates that people are often less willing to cooperate with AI agents than with humans, more readily exploiting AI for personal gain. While prior studies have shown that giving AI agents human-like features influences people's cooperation with them, the impact of AI's assigned gender remains underexplored. This study investigates how human cooperation varies based on gender labels assigned to AI agents with which they interact. In the Prisoner's Dilemma game, 402 participants interacted with partners labelled as AI (bot) or humans. The partners were also labelled male, female, non-binary, or gender-neutral. Results revealed that participants tended to exploit female-labelled and distrust male-labelled AI agents more than their human counterparts, reflecting gender biases similar to those in human-human interactions. These findings highlight the significance of gender biases in human-AI interactions that must be considered in future policy, design of interactive AI systems, and regulation of their use.