You can ask the latest desktop version of Cortana, Microsoft Corp.’s digital assistant, to find the nearest Pizza Hut—but don’t expect it to use any search engine but Microsoft Bing or present the results in any browser but Microsoft Edge.

Cortana no longer can use non-Microsoft browsers or search engines in fulfilling user requests on Windows 10, the software giant said in a blog post Thursday. The restrictions are reminiscent of earlier company moves that once led the U.S. Department of Justice to sue Microsoft for violating...