Shaw was placed in concussion protocol in early December after he was injured against the Colorado Avalanche on Nov. 30. The 28-year-old had 3 goals and 7 assists in 26 games this season.
He was reacquired by Chicago last summer in a trade with the Montreal Canadiens. He is signed through the 2021-22 season with an average annual value of $3.9 million.
Shaw entered the league in 2011 and played his first five seasons with the Blackhawks before he was traded to Montreal.
Smith, who had 4 goals and 7 assists in his first season with the Blackhawks, will have surgery on his back on Friday. The 31-year-old, who was acquired in a July trade with Ottawa in exchange for Artem Anisimov, had missed the last seven games.