Verizon Communications Inc. will pay $1.35 million to settle an investigation with federal regulators over the wireless carrier’s use of so-called supercookies, pieces of software that tracked its customers’ Web usage.

It is the first time the Federal Communications Commission has fined a company related to the use of supercookies, which are inserted into mobile Web traffic to help Verizon and other companies deliver targeted ads. They are called supercookies because they create unique identifiers that cannot be deleted by...