"I am sorely disappointed in the denial of federal approval," Chaney said during a news conference. An exchange is an online marketplace where people can buy health insurance.
Under the federal health law that President Barack Obama signed in 2010, every state is required to have an exchange so people can get coverage starting in January 2014, much of it federally subsidized. States that don't create their own will have one run by Washington.
Chaney submitted an exchange proposal to the U.S. Department of Health and Human Services in mid-November.
Gov. Phil Bryant objects to the federal health care law and sent two letters to Health and Human Services Secretary Kathleen Sebelius trying to block Chaney's proposal. Bryant and Chaney are both Republicans.
Chaney said he had tried to work with the White House to win approval, but "I feel betrayed at this point."
Chaney and his staff had worked on the exchange proposal for several months, spending about $4.5 million in federal money on the effort.
The Chaney-Bryant rift over the health exchange is a rare public dispute between members of the Republican Party, which controls most statewide offices.
"Gov. Bryant has consistently stated his opposition to furthering the implementation of Obamacare in Mississippi, and he believes that establishing a health insurance exchange as defined by the Affordable Care Act will do just that," Bryant spokesman Mick Bullock said Jan. 4.
Associated Press writer Emily Wagster Pettus contributed to this report.