Software sustainability is a key multifaceted non-functional requirement that encompasses environmental, social, and economic concerns, yet its integration into the development of Machine Learning (ML)-enabled systems remains an open challenge. While previous research has explored high-level sustainability principles and policy recommendations, limited empirical evidence exists on how sustainability is practically managed in ML workflows. Existing studies predominantly focus on environmental sustainability, e.g., carbon footprint reduction, while missing the broader spectrum of sustainability dimensions and the challenges practitioners face in real-world settings. To address this gap, we conduct an empirical study to characterize sustainability in ML-enabled systems from a practitioner's perspective. We investigate (1) how ML engineers perceive and describe sustainability, (2) the software engineering practices they adopt to support it, and (3) the key challenges hindering its adoption. We first perform a qualitative analysis based on interviews with eight experienced ML engineers, followed by a large-scale quantitative survey with 203 ML practitioners. Our key findings reveal a significant disconnection between sustainability awareness and its systematic implementation, highlighting the need for more structured guidelines, measurement frameworks, and regulatory support.