Huawei Technologies Co. has been suspended from membership in a global trade group of companies, governments and experts set up to tackle computer security breaches and share information about vulnerabilities.

The Forum of Incident Response and Security Teams, called “First,” was set up in the 1990s to encourage international cooperation in addressing and preventing hacking incidents. It has grown into a sort of informal first responder to big global hacks and cybersecurity incidents. Members share information and intelligence...