"All I know is I'm not responding any emails that I get from Equifax, worried that I'm going to be phished and all my data is going to be stolen," the Tennessee Republican said on CNBC's "Squawk Box." "I've told my entire family, please do not respond to anything that has Equifax on it."
The senator spoke as Equifax shares were halted in premarket trading pending an announcement. The company later said its CEO, Richard Smith, had "retired."
Smith is scheduled to testify before the Senate Banking Committee on Oct. 4.
Corker declined to discuss issues directly related to the breach of data for up to 143 million people.
The stock has suffered since the credit reporting company revealed the hack on Sept. 7, nearly six weeks after it discovered the intrusion.
Since the breach was announced, two other top executives have retired.