Cheney cited "serious health issues" that "have recently arisen in our family" as the reason for her decision.
But her candidacy had raised hackles in the Republican Party and caused a public rift with her sister, Mary, a lesbian, over Liz Cheney's opposition to gay marriage.
In her withdrawal statement, Cheney did not mention those controversies.
"Serious health issues have recently arisen in our family, and under the circumstances, I have decided to discontinue my campaign. My children and their futures were the motivation for our campaign and they will always be my overriding priority," Cheney said. She did not specify those health issues.
She added: "As a mother and a patriot, I know that the work of defending freedom and protecting liberty must continue for each generation. Though this campaign stops today, my commitment to keep fighting with you and your families for the fundamental values that have made this nation and Wyoming great will never stop."
Cheney moved her family from Virginia to Wyoming to run for the seat. Her effort to replace Enzi angered and upset many Republicans and drew virtually no support from Senate Republicans, who rushed to back the Senate veteran and three-term conservative. Enzi's supporters called Cheney a carpetbagger and opportunist.
Sen. Jerry Moran, R-Kan., chairman of the National Republican Senatorial Committee, swiftly expressed support for Enzi moments after Cheney announced last year.
The announcement came as campaigns prepared to release their latest fundraising totals for the last quarter of 2013. In the most recent reports for the period ending Sept. 30, Cheney had more than $795,000 cash on hand while Enzi had more than $1.2 million, according to the Federal Election Commission.
When she announced her campaign, Cheney said it was time for Republicans in Congress to stop "cutting deals" with Democrats and said it was time "for a new generation of leaders."
"We've got to stand and fight, and we have to defend what we believe in. We have to not be afraid of being called obstructionists," Cheney said.
"In my view, obstructing President Obama's policies and his agenda isn't actually obstruction; it's patriotism," Cheney said. "I think we have to stop what he's doing, and then as conservatives, we've got to say, 'Here's what we believe,' and, 'Here's the path forward,' and that's what I intend to lay out in this campaign."
In one television ad, her three daughters — Kate, Elizabeth and Grace — delivered a testimonial in support of their mother's candidacy. She also has two boys, Philip and Richard.
In November, Cheney said she opposed gay marriage, sparking a public feud with her sister, Mary, who is a lesbian and married.
In one of the more public political spats last year, former Wyoming Sen. Alan Simpson said Lynne Cheney, wife of the former vice president and Liz's mother, told him to "shut up" during a reception.
Both Simpson and Lynne Cheney said the dispute centered on Simpson's earlier refusal to sign a football for Cheney's 15-year-old granddaughter at a recent Wyoming fundraiser. Simpson was supporting Enzi.
The dispute with Simpson underscored Cheney's struggle to win over establishment Republicans in Wyoming where she secured some support from tea party activists but came up short with the state's prominent Republicans.
Most of her major in-state supporters were family friends and past supporters of Dick Cheney.
Wyoming Republican Party Chairwoman Tammy Hooper said she talked to Cheney officials Sunday about the campaign being called off. Hooper said she didn't hear any more specifics about the health issue.
"There were some health issues that came up, serious ones," Hooper said Monday. "And they had many phone calls to make, certainly. They said they would be back in touch."
Cheney's decision was first reported by CNN, The New York Times and Politico.
Associated Press writer Mead Gruver in Cheyenne, Wyo., contributed to this report.
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