The surgery could impact Smith's 2016 NFL draft status if he still decides to forgo his senior season, according to league sources. He has been projected as a potential top five or 10 draft selection.
Smith is still expecting to apply for draft eligibility, school sources said.
Smith suffered what Notre Dame coach Brian Kelly described as a "significant" left knee injury early in the Fiesta Bowl against Ohio State.
Smith was the 2015 Butkus Award winner as the nation's top collegiate linebacker.