Palace sources said Mubarak al-Fadil al-Mahdi, who served as al-Bahir's second vice-president, was sacked on Wednesday.
Al-Mahdi took office almost two years ago after having led a breakaway group from the mainstream opposition Umma party.
He and a group of rebel Umma party officials returned to Sudan from exile and accepted ministerial portfolios, including the information and international cooperation posts.
He was interior minister in the country's democratically-elected government that was toppled by al-Bashir in a 1989 bloodless coup.
Wednesday's presidential decree targeted only al-Mahdi without mentioning his colleagues.