Smith notched an assist and three shots on goal in Wednesday's 3-2 loss to the Maple Leafs.
Smith (upper body) will not play Friday against the Canucks.
Smith (rest) is slated to play Monday versus the Penguins, per Zach Gilchriest of the Predators' official site.
Smith will not play in Saturday's game versus the Blue Jackets due to roster management reasons.
Smith scored his ninth goal of the season in Saturday's 7-4 loss to the Avalanche.
Smith signed a two-year, $2 million contract extension with Nashville on Wednesday.
Smith (illness) is not in the lineup for Tuesday's game versus the Blackhawks.
Smith scored his first two goals of the season, including the game-winner, in Thursday's 4-1 victory over the Rangers.
Smith (upper body) is healthy for training camp, Nick Kieser of Nashville Hockey Now reported Wednesday
Smith (upper body) is not considered close to returning to action according to general manager David Poile, Robby Stanley of 102.5 The Game reports Tuesday.