Speaking at the ceremony, the leftist leader said she was taking the lead of a "broken" country - but vowed to pursue social justice and transparency.
Ms Castro, 62, has promised to tackle powerful drug trafficking gangs and liberalise strict abortion laws.
But her agenda has been undermined by a feud in her Libre (Free) Party.
Ms Castro's husband, Manuel Zelaya, ruled the country from 2006 until 2009, when he was ousted by a coup. She ran for office twice in the years following his removal from power, before her victory in the election last November.