It will mean a minimum of roughly six months away from the playing field," he said in a statement from his club side Cardiff Blues.
"It will also allow me to continue my focus on the final year of my degree in medicine and the finals I'll be sitting next March."
Roberts scored a memorable try in the Six Nations championship win against Italy last month as Wales steamrollered their way to a grand slam.
His injury is also a blow to the Blues, who sacked former Wales player and fellow centre Gavin Henson on Monday following a drinking incident on a flight.
They visit Ireland's defending champions Leinster in a Heineken Cup quarter-final this weekend.