Justice Olukayode Ariwoola, 64, succeeds Muhammad as the most senior judge on the bench. Buhari said Muhammad was due to retire next year but ill heath had forced him to step down on Monday.
The Senate will need to confirm Ariwoola to become substantive Chief Justice, who will chair the Supreme Court, the highest tribunal in the West African country.
Judges of Nigeria's Supreme Court serve until the age of 70 years when they have to retire.
The Supreme Court hears disputes on various cases including election results. Nigerians will go to the polls next February to elect Buhari's successor.
Buhari appointed Muhammad in 2019. Under his leadership the Supreme Court dismissed an appeal by the main opposition candidate Atiku Abubakar to overturn the result of the 2019 presidential election in which Buhari was returned to office.
This month, Nigeria's ruling party chose Bola Tinubu, to be its candidate to replace Buhari in next year's vote. He will face Abubakar, a former vice president and veteran politician who is the main opposition People's Democratic Party's (PDP) flagbearer.
(Reporting by Camillus Eboh and Felix Onuah;Writing by MacDonald Dzirutwe and Chijioke Ohuocha;Editing by James Macharia Chege, Bernadette Baum and Susan Fenton)
