China’s clampdown on the cyber tunnels used to burrow through its Great Firewall may do more than further restrict internet access—it also threatens to make emails and data transmissions by foreign companies more vulnerable to government surveillance, security analysts say.

Companies, institutions and individuals use virtual private networks, or VPNs, to send secure emails, transmit data and access websites blocked in China. The country’s Ministry of Industry and Information Technology served notice last year that access to...