He tweeted that Patrick Shanahan has pulled out of consideration "so that he can devote more time to his family".
Shanahan, who will be replaced by Army Secretary Mark Esper, had not yet been nominated for the cabinet post.
It comes as Shanahan publicly addressed allegations of domestic violence.
Trump told reporters Shanahan submitted his withdrawal on Tuesday morning, the BBC reported.
"I didn't ask him to withdraw, but he walked in this morning and said it was going to be a rough time for him," Trump said, adding that he first heard of the "unfortunate" allegations on Monday.
Earlier on Tuesday, USA Today reported the FBI was investigating a 2010 incident in which Shanahan and his ex-wife accused each other of assault.
Minutes after Trump's announcement, the Washington Post published an interview with Shanahan in which he discussed a 2011 incident when his son, then 17, reportedly beat his mother with a baseball bat, fracturing her skull.
In a statement announcing his resignation, Shanahan called it "unfortunate that a painful and deeply personal family situation from long ago is being dredged up and painted in an incomplete and therefore misleading way".
He said he did not want his three children "to relive a traumatic chapter in our family's life and reopen wounds we have worked years to heal".
Shanahan added: "I would welcome the opportunity to be secretary of defense, but not at the expense of being a good father."
On Monday, he told the Washington Post that he regretted a legal memo he penned shortly after the alleged attack on his ex-wife.
He wrote that the "use of a baseball bat in self-defence will likely be viewed as an imbalance of force" and that "Will's mother harassed him for nearly three hours before the incident".
Before joining the Trump White House, Shanahan had worked as an executive at Boeing, the US aerospace company which holds many US defence department contracts.
He took over six months ago after the resignation of former Defence Secretary James Mattis.
( With inputs from IANS )