The decision increases the Republican Party's chance of gaining control of the upper house. Walsh was the state's lieutenant governor when Gov. Steve Bullock, also a Democrat, named him to replace Max Baucus, who had held the seat since 1978.
Walsh said he plans to serve in the Senate until the term ends. But said the plagiarism scandal is a "distraction."
"I am ending my campaign so that I can focus on fulfilling the responsibility entrusted to me as your U.S. senator," Walsh said in a statement. "You deserve someone who will always fight for Montana, and I will."
Walsh served for three decades in the Montana National Guard, becoming its commander in 2008. He also spent time on active duty in Iraq.
But the New York Times reported last month that Walsh used others' work in his thesis at the Army War College without attributing it. The college, which granted Walsh a master's degree in 2007, is conducting its own investigation.
While many of the western states are now solidly Republican, the party has not held Walsh's seat for more than a century. But Rep. Steve Daines, the party's candidate, was believed to have a good chance of defeating Walsh.
"Steve Daines is one of the strongest Senate candidates in the country, was in the process of defeating Sen. Walsh, and will defeat whichever band-aid candidate Democrats can persuade to get in the race," said Brad Dayspring, spokesman for the National Republican Senatorial Committee.