The rapid development of information and communication technologies (ICTs) and cyber–physical systems (CPS) has paved the way for the increasing popularity of smart products. Context-awareness is an important facet of product smartness. Unlike artifacts, various bio-systems are naturally characterized by their extraordinary context-awareness. Biologically inspired design (BID) is one of the most commonly employed design strategies. However, few studies have examined the BID of context-aware smart products to date. This paper presents a structured design framework to support the BID of context-aware smart products. The meaning of context-awareness is defined from the perspective of product design. The framework is developed based on the theoretical foundations of the situated function–behavior–structure ontology. A structured design process is prescribed to leverage various biological inspirations in order to support different conceptual design activities, such as problem formulation, structure reformulation, behavior reformulation, and function reformulation. Some existing design methods and emerging design tools are incorporated into the framework. A case study is presented to showcase how this framework can be followed to redesign a robot vacuum cleaner and make it more context-aware.