Muhammad Ali Bogra was born in East Bengal. He studied at the Calcutta University and in 1937 he was elected to the Bengal legislative assembly. In 1943, Bogra became parliamentary secretary to Khawaja Nazimuddin, the then Chief Minister of Bengal. Later in 1946, he became Finance and Health Minister of the province.
After the establishment of Pakistan, he was appointed Ambassador to Burma in 1948, High Commissioner to Canada in 1949 and Ambassador to USA in 1952.
Muhammad Ali Bogra was appointed Prime Minister in April 1953 by Ghulam Muhammad. After the dissolution of the Constituent Assembly in 1954 by the governor-general, Bogra was again invited to form a new cabinet call “ministry of all talents.”
Muhammad Ali Bogra was replaced by Chaudhary Muhammad Ali in August 1955 after the second constituent Assembly was elected. Muhammad Ali again resumed his assignment as ambassador in the USA.