An electronic device may be provided with a conductive housing sidewall and a phased antenna array that conveys radio-frequency signals at frequencies greater than 10 GHz. Each antenna in the array may radiate through a respective aperture in the sidewall. The antenna module may include a folded flexible printed circuit having a first portion and a second portion that extends from an end of the first portion and that is folded with respect to the first portion. The antennas in the phased antenna array may have antenna resonating elements that are distributed between the first and second portions. Forming the antenna module from a folded flexible printed circuit in this way may serve to minimize the thickness of the antenna module, thereby allowing the antenna module to fit between a ledge of the sidewall and a rear housing wall without occupying excessive space within the device.