Al-Sabah was born on 10 June 1955 and is the son of the late Emir of Kuwait, Sheikh Sabah III Al-Salim Al-Sabah. His elder brother is Sheikh Salem Sabah Al-Salem Al-Sabah, former defense and interior minister. Sabah received a bachelor's degree in economics from Claremont McKenna College. In addition, he holds a master's degree and a PhD in economics from Harvard University.
Al-Sabah was a professor of economics at Kuwait University between 1979 and 1985, before working at the Kuwait Institute for Scientific Research from 1987 to 1988. In 1993, he was appointed ambassador of Kuwait to the United States. He remained in this position until 14 February 2001 when he was appointed state minister for foreign affairs. On 11 February 2005, Sheikh Mohammad was appointed as Kuwait's deputy prime minister while retaining the position of minister of foreign affairs. He resigned from office on 18 October 2011 in protest of alleged corruption in Kuwait's government. He was replaced by another member of the Sabah Family, Sabah Al Khalid Al Sabah in the post. After leaving office, Al-Sabah began to work as a visiting fellow at Oxford University.