Ashley, 30, is a social worker and career development and education liaison in the education office for the Delaware Department of Services for Children, Youth and Their Families.
She married Dr Howard David Krein, 45, a son of Bunny Lipner Krein and Stanley Krein at a church in Greenville, Delaware.
Biden and his wife Jill issued a statement saying the couple's close family and friends attended the private ceremony.
"We're happy to welcome Howard into our family, and we wish them all the best in their new life together," the statement said.
Ashley in involved in developing programmes for children in the juvenile-justice, foster-care and mental-health systems. She graduated from Tulane University and received a Master's of Social Work from the University of Pennsylvania.
Howard is an otolaryngologist and plastic surgeon at Thomas Jefferson University Hospitals in Philadelphia. He is also an assistant professor of otolaryngology/head and neck surgery and a director of the Herbert Kean Center for Facial Aesthetics there.
