"As a friend and colleague, I offer my support and help to him in any way I can," Risch said in a statement. "Senator Crapo has worked hard on behalf of Idahoans for many years and I have full confidence that Senator Crapo will continue his dedicated and unselfish service to the people of Idaho."
Risch is Catholic.
Idaho's two U.S. representatives, Raul Labrador and Mike Simpson, are Mormons, though Simpson has been open with constituents and media about drinking and smoking cigarettes.
Neither Republican immediately responded to a request for comment.
Idaho politicians getting arrested for drunken driving is nothing new: Gov. C.L. "Butch" Otter was arrested in the early 1990s, when he was lieutenant governor; Democratic state Sen. Edgar Malepeai of Pocatello was arrested for DUI in 2009; and former state Sen. John McGee, a Caldwell Republican, was arrested on Father's Day 2011 after driving drunk and taking a car that didn't belong to him.
But none of them were Mormon.
Crapo raised the stakes by projecting an image of a diligent member of the faith and - at least outwardly - following church founder Joseph Smith's 1833 revelation in which he advised members that "strong spirits are not for the belly."
The U.S. Senate adjourned last week and wasn't expected to resume until Wednesday; it's unclear why Crapo had remained in Washington, D.C., ahead of the Christmas holiday.
According to the police report, he was alone in his car. It wasn't immediately clear where he'd been or where he was going when he was stopped.
Crapo was a Mormon bishop at 31 and has showed no public signs of a break from his church's teachings.
Church members must follow its guidance - including its rules on alcohol - to participate fully in the faith's rituals, including temple activities that are central to the religion.
Phone calls Monday to Mormon headquarters in Salt Lake City were not returned.
Crapo, first elected in 1998, is expected to take over the top Republican spot next year on the Senate Banking Committee. He also serves on the Senate's budget and finance panels and was a member of the so-called "Gang of Six" senators who worked in 2011 toward a deficit-reduction deal that was never adopted by Congress.
The 2010 bill he sponsored on cutting taxes for brewers ultimately stalled.