BRUSSELS—Microsoft Corp.’s Skype subsidiary has been summoned to appear before a Belgian court for refusing to allow authorities to wiretap communications between two criminal suspects, in a case that could decide whether the online phone-call and messaging service should be treated as a telecom company, a court spokesman said Tuesday.

The case comes as Europe’s incumbent telecom operators gripe that online communication services, such as Skype and WhatsApp, are receiving beneficial treatment and aren’t taxed or regulated in...