Building autonomous agents able to grow open-ended repertoires of skills across their lives is a fundamental goal of artificial intelligence (AI). A promising developmental approach recommends the design of intrinsically motivated agents that learn new skills by generating and pursuing their own goals - autotelic agents. But despite recent progress, existing algorithms still show serious limitations in terms of goal diversity, exploration, generalisation or skill composition. This perspective calls for the immersion of autotelic agents into rich socio-cultural worlds, an immensely important attribute of our environment that shapes human cognition but is mostly omitted in modern AI. Inspired by the seminal work of Vygotsky, we propose Vygotskian autotelic agents - agents able to internalise their interactions with others and turn them into cognitive tools. We focus on language and show how its structure and informational content may support the development of new cognitive functions in artificial agents as it does in humans. We justify the approach by uncovering several examples of new artificial cognitive functions emerging from interactions between language and embodiment in recent works at the intersection of deep reinforcement learning and natural language processing. Looking forward, we highlight future opportunities and challenges for Vygotskian Autotelic AI research, including the use of language models as cultural models supporting artificial cognitive development.