President Donald Trump also withdrew Shanahan's nomination for the job at his request on Tuesday.
He appointed Army Secretary Mark Esper to be the Acting Defence Secretary. The Defence Department has not had a permanent head since last December when Jim Mattis quit in protest against Trump's plans to withdraw troops from Syria.
Police reports of the domestic incident said Shanahan was the victim in the 2010 incident.
According to the Seattle police reports posted by the USA Today newspaper, which broke the story of his domestic problems, Shanahan had not been accused of attacking his then-wife but she was said to have hit him leaving a black eye and a bleeding nose.
Although she was arrested, she was not prosecuted. The police report said that both of them had been drunk.
Despite the police report clearing him, he would have had a difficult - and embarrassing - time during Senate confirmation hearings, especially because of the heightened sensitivity to domestic violence or incidents involving women.
Brett Kavanaugh's confirmation as a Supreme Court judge was nearly torpedoed last year because of accusations of misbehaviour with girls when he was a high school student.
Compounding Shanahan's problem, a year later his then 17-year-old son attacked his mother with a baseball bat, according to The Washington Post.
Shanahan told the daily that he had prepared a memo that his son acted in self-defence but now regretted writing it.
Shanahan and Kimberly Jordinson divorced after a bitter court battle.
"I believe my continuing in the confirmation process (for Defence Secretary) would force my three children to relive a traumatic chapter in our family's life and reopen wounds we have worked years to heal," Shanahan said in a statement on Tuesday.
"Ultimately, their safety and well-being is my highest priority".
Trump told reporters that he did not ask Shanahan to withdraw his nomination but that he had volunteered.
Shanahan was the Deputy Defence Secretary under Mattis and before that had been a senior executive at Boeing, where he had worked for over 30 years.
His departure comes at a crucial time for the US as tension mount with Iran, which announced on Monday that it had increased production of low-grade uranium and, unless Europeans intervened, it would exceed the limits set by the multi-party nuclear agreement that Trump has renounced.
Shanahan had announced on Monday that he was moving 1,000 troops to the Middle East as the US blamed Iran for the attacks on two petroleum tankers in the Gulf of Oman on June 13.
This was in addition to the 1,500 sent to the region last month along with an aircraft carrier and bombers and fighter jets.
Secretary of State Mike Pompeo, a former Army captain and the head of the Central Intelligence Agency, is stepping into the breach, though without formal charge of Defence.
He visited the Central Command headquarters in Florida on Tuesday to meet the generals there.
Pompeo told reporters that they "spoke about the challenges in Iran" and also about Shanahan's decision to send more troops to the region.
"The purpose of my visit was to come down here and make sure that the State Department and the Department of Defence were deeply coordinated across a whole broad range of issues," he added.
(Arul Louis can be reached at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )