Weber leads the Predators in points and "will be evaluated on a daily basis with no timetable on his return," the team posted on its Twitter account.
The Predators' captain was hurt in a game at Dallas Friday.
Weber, 26, leads Nashville in points (29), assists (21) and plus-minus (+14).
Liles, 31, was placed on injured reserve by Toronto with concussion-like symptoms.
Liles absorbed a hard hit from Buffalo Sabres forward Paul Gaustad in a Dec. 22 game and didn't practice Monday or Tuesday.
The veteran blueliner has produced four goals and 21 points in 34 games this season, his first with Toronto.