Magnetic resonance imaging (MRI) compatible robots can assist physicians with the insertion of biopsy needles and needle-like therapeutic instruments directly into millimeter-size tumors, using MR images as feedback. However, MRI systems present a challenging environment with high magnetic fields and limited space, making the development of MRI-compatible robots complex. This paper presents an MRI-compatible pneumatic actuation technology consisting of molded polymer structures with embedded air-muscles operated in a binary fashion. Along with its good positioning accuracy, the technology presents advantages of compactness, perfect MRI-compatibility, simplicity and low cost. Here, we specifically report the design and validation of a transperineal prostate cancer manipulator prototype that has 20 embedded air-muscles distributed in four star-like polymer structures. These compliant structures are made of silicone elastomer, using lost-core injection molding. Low motion hysteresis and good precision are achieved by designing molded joints that eliminate sliding surfaces. An effective design method for such embedded polymer air-muscles is proposed, using a manipulator model and four air-muscle design models: geometrical, finite elements, uniaxial analytic, and experimental. Binary control of each air-muscle ensures stability and accuracy with minimized costs and complexity. The prototype is found MRI-compatible with no observable effects on the signal-to-noise ratio and, with appropriate image feedback, is found to reach targets with precision and accuracy under 0.5 mm. The embedded approach reveals to be a key feature since it reduces hysteresis errors by a factor of ≈7 compared to a previous nonembedded version of the manipulator. The successful validation of this binary manipulator opens the door to a new design paradigm for low cost and highly capable pneumatic robots.