The move was ordered on Thursday by the Public Regulation Department's Chief of Staff Daniel Mayfield.
Chavez told the Albuquerque Journal that he expects "an expeditious investation" but would not elborate on the details of the inquiry.
"I will fully cooperate with any and all investigation the PRC will be doing and look forward to resolving any and all issues," Chavez said.
PRC commissioner Sandy Jones said the investigation is "strictly a personnel issue."
"To protect everyone's rights, we're not going to comment. We are not going to discuss it," Jones said.
Chavez was appointed to the post in 2006 after his predecessor Eric Serna resigned after it was disclosed that a state government contractor had contributed $129,000 to a charity which was headed by Serna before he was ordered to resign from the Con Alma Health Foundation board.
In 2008, Sernas Deputy Insurance Superintendent Joe Ruiz was convicted for shaking down insurance companies and sentenced to four years in prison for corruption. His convictions were upheld by the 10th Circuit Court of Appeals last month.