An electronic device may have a camera module for acquiring still and video digital images of a subject. A light source such as a light-emitting diode may serve as a flash for the camera module. A shutter may be mounted above the light-emitting diode. When the light-emitting diode is not being used to produce a flash of light for illuminating the subject, the shutter may be closed to block the light-emitting diode from view by a user. During image acquisition operations in which it is desired to illuminate the subject, the shutter may be opened to allow light from the light-emitting diode to exit the electronic device. The electronic device may have a touch screen display with an active region and an inactive region. The camera module and light source may be mounted under a portion of the inactive region of the display. The shutter may include a filter structure.