"He is in good spirits and talking with his family at the hospital," Dr. Timothy Gardner said in a statement issued through the White House later in the day. "He is fully alert, in stable condition and has full motor and speech skills."
A state trooper was stationed at the main entrance of the hospital and several black SUVs and men in suits with earpieces were nearby.
The vice president had traveled to Delaware on Monday afternoon for a previously scheduled trip. He did a round of morning show interviews from Wilmington Tuesday morning, and was supposed to return to Washington later in the day for his weekly lunch with President Barack Obama and a series of meetings on Afghanistan.
The White House did not respond to questions about whether the vice president would still attend.
Dr. Jill Biden's scheduled tour of a women's health facility in Washington Tuesday afternoon was postponed. Beau Biden was scheduled to deliver a speech Tuesday night at the University of Delaware, but that was canceled too.
Beau Biden returned last year from a yearlong deployment to Iraq with his Army National Guard unit. He was a captain and military lawyer in the 261st Theater Tactical Signal Brigade.
He had considered running this year for the Senate seat his father held before becoming vice president, but decided against it.
He said when he announced his decision in January that he needed to remain focused as attorney general on a high-profile criminal scandal involving a pediatrician accused of sexually assaulting several patients. Prosecutors believe Dr. Earl Bradley, who was arrested in December, may have molested more than 100 children over the past decade.
Biden's decision was a surprise, given that his father's longtime confidant and former Senate chief of staff, Ted Kaufman, was appointed to the seat essentially to keep it warm for the son until this year's election.
But longtime Republican Rep. Mike Castle, a two-term governor and one of the most successful politicians in Delaware history, entered the Senate race in October, dramatically increasing the likelihood of a fierce contest.
Beau Biden's decision left the seat his father held for 36 years vulnerable.
The elder Biden was away from that seat for seven months in 1988 after undergoing surgery for brain aneurysms.
More than a decade earlier, in 1972, he lost his wife and infant daughter when a tractor-trailer broadsided their station wagon when they were out getting a Christmas tree. Beau and his brother Hunter were critically injured but recovered.
The vice president devoted himself to caring for his two sons as a single father and still will not work Dec. 18, the date it happened. The elder Biden seldom speaks of the tragedy, but remains sensitive about anything having to do with his children's welfare.
Beau Biden recalled the accident when introducing his father at the 2008 Democratic National Convention in Denver.
"I was just short of 4 years old. One of my earliest memories was being in that hospital, Dad always at our side. We, not the Senate, were all he cared about," Biden said. His father was sworn in to the U.S. Senate at the hospital, at his bedside, he said.
At the convention, the vice president said in return: "Beau, I love you. I am so proud of you. I'm so proud of the son you've become. I'm so proud of the father you are."
Beau Biden, who is married with two young children, has worked as an attorney in private practice. He also worked for the Justice Department between 1995 and 1997 and as an assistant U.S. attorney from 1997 to 2002.