The 56-year-old Rabier and the federation had parted on amicable terms, federation official Solo Rajaonarivelo told AFP.
Rabier, who has coached several second-division French teams and the national team of Burkina Faso, was hired in April 2010 with the aim of securing qualification for the next African Cup of Nations in 2012 in Gabon and Equatorial Guinea.
Madagascar’s campaign, however, kicked off with two defeats, away to Nigeria (2-0) and at home to Ethiopia (0-1).
Rabier’s replacement Mosa is a former captain of the national team in the 1970s and was previously national coach between 1987-90 and in 1994. His first game back in charge will be at home against Guinea on March 27.