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Abstract Minimally invasive robotic surgery often requires functional tools that can change their compliance to adapt to the environment and surgical needs. This paper proposes a submillimeter continuous variable stiffness catheter equipped with a phase‐change alloy that has a high stiffness variation in its different states, allowing for rapid compliance control. Variable stiffness is achieved through a variable phase boundary in the alloy due to a controlled radial temperature gradient. This catheter can be safely navigated in its soft state and rigidified to the required stiffness during operation to apply a desired force at the tip. The maximal contact force that the catheter applies to tissue can be continuously modified by a factor of 400 (≈20 mN–8 N). The catheter is equipped with a magnet and a micro‐gripper to perform a fully robotic ophthalmic minimally invasive surgery on an eye phantom by means of an electromagnetic navigation system.