Msezane was born in Springs, South Africa on 31 December 1938, into a Zulu family. His father, Albert Msezane, was from Piet Retief, while his mother was from eSwatini (formerly Swaziland). Msezane lived on a farm with his grandmother and worked as a shepherd. In search of better opportunities, his parents moved to Johannesburg, where they raised him and his brother, Richard, and managed a successful livestock trading business.
In his early schooling in St. Louis Catholic School, Msezane already demonstrated an interest and aptitude in mathematics. He attended Thlakula school from grades seven to nine, and graduated from Inkamana high school in 1959. Due to apartheid policies, he was not able to enrol in any White-only university. Instead, with a Rotary International Scholarship, he enrolled in University of Fort Hare in 1960 and obtained a B.Sc.-Honours degree in physics in 1965. In the same year, he accepted a World University Scholarship to pursue a Ph.D. at University of Saskatchewan in Canada, where he research focus was on the structure of the deuteron.
After obtaining his M.Sc. in theoretical nuclear physics in 1968, Msezane returned to Johannesburg to complete his doctoral degree at University of the Witwatersrand. His research was interrupted by apartheid policies, and he had to return to Canada in 1969 to write his dissertation on collision theory at the University of Western Ontario. There, he married Gail P. Msezane, whom he had met at the University of Saskatchewan. He obtained his Ph.D. in physics in 1974.