Embodied intelligence reflects the ability of an agent to interact with its environment through its body to gain intelligence and autonomy. Such a concept has become popular in recent years for the design of robotic systems. This paper generalises the embodied intelligence concept to Additive Manufacturing (AM) to provide a new understanding of the technology with inspirations from biological production processes including organism growth and animal construction. Morphology-based embodied intelligence is analysed on the design and manufacturing aspects for delivering intelligent products (including robots) while embodied artificial intelligence (AI) (foundation models) is discussed for the printer itself. The paper opens a new perspective for AM research.