Smith, a first-round draft pick (No. 6 overall), sustained a small fracture in the foot during a non-contact drill in his third workout since signing his deal, another major setback to his chances of winning the Bengals' starting right tackle job this season.
La Canfora reports that Smith likely will be off the field for seven to 10 days and then is scheduled to resume normal work.
A long contract impasse forced Smith to miss training camp and the first three preseason games. He agreed to a four-year, $26 million deal that includes $21 million guaranteed on Sunday and worked out with the team later in the day, hoping to play in Thursday night's preseason finale against the Indianapolis Colts.
Cincinnati's offensive line has undergone an overhaul during the offseason. The team made changes at center and both tackle positions, hoping to upgrade an offense that finished last in the league in 2008.
The priority is protecting quarterback Carson Palmer, who was hit often last year. He broke his nose during the preseason and tore a ligament and a tendon in his passing elbow during the regular season, forcing him to miss 12 games.
Palmer suffered a moderate sprain in his left ankle during the first preseason game this year and has missed the last two. He took snaps with the starting offense Tuesday for the first time since he got hurt.
"He looked remarkably improved," Lewis said. "He looked pretty good. He was moving better."
Palmer would like to play in the preseason finale; Lewis will make a decision on that shortly before the game starts.
"We're going to play out what's best for Carson as we go forward," Lewis said. "It was good to see him get back and involved in the things we'll do today and tomorrow, and then when we start next week. The goal is to have him ready to go full speed by Monday."
The Associated Press contributed to this report.