The Syracuse Republican said in a statement he decided to quit after discussing his options with his family and friends.
"My heart weighs heavy. I have a tremendous amount of respect for the legislative process, my legislative colleagues and for my constituents," said Killpack, 41.
"At this time, the Legislature would be a distraction from what is most important and, frankly, I find that I have become a distraction to the Legislature. In light of that, I have decided to tender my resignation ... effective immediately."
Killpack, whose father was killed by a drunken driver when Killpack was a teenager, supported and sponsored drunken-driving measures during his six years in office.
The Utah Highway Patrol said a trooper pulled over Killpack early Friday in Salt Lake City after observing his vehicle driving erratically.
The trooper detected a "strong odor of alcohol" and asked Killpack to perform field sobriety tests. Killpack did the field tests but refused to take a breath test. The patrol got a warrant to take blood, and Killpack was booked into jail and later released. The patrol has said blood results could take anywhere from two weeks to a month.
Killpack was appointed to the state Senate in 2003, then won election in 2004. He earned a second four-year term in 2008. He was elected to the No. 2 position in Senate GOP leadership last year and was viewed as a rising star in Utah politics.
State GOP Chairman Dave Hansen criticized Killpack in a statement Friday, saying it was "inexcusable for anyone, especially those in positions of public trust, to violate our laws."
Senate President Michael Waddoups, R-Taylorsville, said he did not advise Killpack on whether to quit.
"I told him it was a personal matter, that he should decide it in consultation with his family, and I'd support him if he stayed and I'd support him if he left," Waddoups told the Salt Lake Tribune.
But Waddoups added it would be tough for Killpack to face his conservative constituents. Killpack is a member of the Mormon church, which counsels its members not to drink alcohol.
Killpack apologized in a statement Friday, saying he must be held accountable for his actions.
He had attended a fundraiser for state Rep. Greg Hughes, R-Draper, on Thursday night, but no alcohol was served at the event. Former state Rep. Mark Walker was his passenger when he was pulled over.
