An electronic device may have a housing in which a display and other components are mounted. Audio components such as a speaker and microphone and other electrical components may be mounted in an interior portion of the housing. A housing port may be formed from one or more openings that pass through the housing. The audio component or other component may be aligned with the housing port. A shutter may be interposed between the audio component and the housing port. The shutter may have an electrically controlled positioner that is used to position a movable shutter member. The shutter may be closed by placing the shutter member in a position in which the housing openings are blocked, thereby preventing intrusion of contaminants into the interior portion of the housing. The shutter may be opened by placing the shutter member in a position in which the housing openings are unblocked, thereby allowing sound to pass through the housing port.