A stabilizer folding structure and a handheld stabilizer. a stabilizer folding structure for rotationally connecting the motor base and the rocker arm such that the motor base and the rocker arm have an unfolded first state and a stored second state during relative rotation, comprising: an elastic member, applying An elastic force for abutting the motor base and the rocker arm; and a snap structure at a position where the motor base abuts the rocker arm, in the first state and the second state, The snap structure is engaged to restrict relative rotation of the motor base and the rocker arm. In other states, the snap structure is disengaged such that the motor base and the rocker arm are relatively rotatable. The folding structure of aspects of the invention facilitates the folding and storage of the stabilizer, and is convenient for the user to use.