A U.S. company that makes Internet-blocking gear acknowledges that Syria has been using at least 13 of its devices to censor Web activity there—an admission that comes as the Syrian government cracks down on its citizens and silences their online activities.

Blue Coat Systems Inc. of Sunnyvale, Calif., says it shipped the Internet "filtering" devices to Dubai late last year, believing they were destined for a department of the Iraqi government. However, the devices—which can block websites or record when people visit them—made...