Mr. Enzi is the fourth senator to announce his intention to step down, following two other Republicans, Pat Roberts of Kansas and Lamar Alexander of Tennessee, and one Democrat, Tom Udall of New Mexico.
His seat, in a state that President Trump won by 46 points in 2016, is likely to remain in Republican hands. The last Democratic senator to represent Wyoming left office in the 1970s.
It is unclear if Representative Liz Cheney, the No. 3 House Republican who once challenged Mr. Enzi in a primary race, will take another shot at the seat — a decision that would reshape Republican leadership in the House. Mr. Enzi, in his remarks, said he could see Ms. Cheney becoming speaker one day. Ms. Cheney has also told people in recent months how much she is enjoying the House, where her father, former Vice President Dick Cheney, once served.
Mr. Enzi “brought our state’s values to the nation’s capital,” Ms. Cheney said in a statement, “fighting for a smaller, less obstructive, and more efficient federal government that would allow people to grow and thrive. He recognized that empowering people, not politicians, was the best way to expand opportunity, and he worked tirelessly toward that goal.”