Cheney cited "serious health issues" that "have recently arisen in our family" as the reason for her decision, according to a statement quoted in The New York Times.
The GOP official confirming Cheney's decision spoke on condition of anonymity because the official was not authorized to speak on the record.
Cheney moved her family from Virginia to Wyoming to run for the seat. Her effort to replace Enzi, a Senate veteran, angered and upset many Republicans and her campaign faced a number of problems.
In November, Cheney said she opposed gay marriage, sparking a public feud with her sister, Mary, who is a lesbian and married.
"My children and their futures were the motivation for our campaign and their health and well-being will always be my overriding priority," Cheney's statement said.
Cheney's decision was first reported by CNN, The New York Times and Politico.
She did not immediately respond to a request for comment from The Associated Press.
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