Thin foldable origami mechanisms allow reconfiguration of complex structures with large volumetric change, versatility, and at low cost; however, there is rarely a systematic way to make them autonomously actuated due to the lack of low profile actuators. Actuation should satisfy the design requirements of wide actuation range, high actuation speed, and backdrivability. This paper presents a novel approach toward fast and controllable folding mechanisms by embedding an electromagnetic actuation system into a nominally flat platform. The design, fabrication, and modeling of the electromagnetic actuation system are reported, and a 1.7 mm-thick single-degree-of-freedom (DoF) foldable parallel structure reaching an elevation of 13mm is used as a proof of concept for the proposed methodology. We also report on the extensive test results that validate the mechanical model in terms of the loaded and unloaded speed, the blocked force, and the range of actuation.