With the global rollout of fifth generation (5G) networks, it is necessary to look beyond 5G and envision 6G networks. 6G networks are expected to have space-air-ground integrated networks, advanced network virtualization, and ubiquitous intelligence. This article presents an artificial intelligence (AI)-native network slicing architecture for 6G networks to enable the synergy of AI and network slicing, thereby facilitating intelligent network management and supporting emerging AI services. AI-based solutions are first discussed across the network slicing life cycle to intelligently manage network slices (i.e., AI for slicing). Then network slicing solutions are studied to support emerging AI services by constructing AI instances and performing efficient resource management (i.e., slicing for AI). Finally, a case study is presented, followed by a discussion of open research issues that are essential for AI-native network slicing in 6G networks.