Donaldson said he didn't immediately know what Crapo's blood alcohol level was, where he was coming from or the type of vehicle he was driving.
The 61-year-old Crapo (KRAY'-poh) has a Jan. 4 court date.
"I am deeply sorry for the actions that resulted in this circumstance," Crapo said in a statement Sunday night. "I made a mistake for which I apologize to my family, my Idaho constituents and any others who have put their trust in me. I accept total responsibility and will deal with whatever penalty comes my way in this matter. I will also undertake measures to ensure that this circumstance is never repeated."
A Crapo spokesman declined to comment on the circumstances surrounding his arrest.
Currently in his third term, Crapo has been in the Senate since 1998, and served for six years in the U.S. House of Representatives before that. He was easily re-elected in 2010, and won't have to run again until 2016.
In Congress, Crapo has built a reputation as a staunch social and fiscal conservative. It has been expected he would take over the top Republican spot next year on the Senate Banking Committee. He also serves on the Senate's budget and finance panels. Crapo was a member of the so-called "Gang of Six" senators that worked in 2011 toward a deficit-reduction deal that was never adopted by Congress.
A Mormon who grew up in Idaho Falls, Idaho, Crapo was named a bishop in the church at age 31. He is an attorney who graduated from Brigham Young University and Harvard Law School. He has five children with his wife, Susan, and three grandchildren.
The Mormon Church prohibits the use of alcohol, as well as caffeine and other mind-altering substances.
Associated Press writers Norman Gomlak in Atlanta and Josh Lederman in Washington contributed to this report.