CINCINNATI — Rookie right tackle Andre Smith broke his left foot during practice Tuesday, only two days after he ended his holdout with the Cincinnati Bengals.

The first-round pick 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 starting job this season.

‘‘Our medical staff tells me the injury will not require surgery,’’ coach Marvin Lewis said. ‘‘It’s too soon to closely predict how long it will be before he can return to practice, but it looks like he’s going to miss a few weeks.’’

The Bengals took Smith with the sixth overall pick, expecting him to start at right tackle.

A long contract impasse forced him to miss training camp and the first three preseason games. He agreed to a four-year deal that includes $21 million guaranteed on Sunday and worked out with the team later in the day, hoping to play in the final preseason game Thursday against Indianapolis.

Now, the Bengals will keep second-year lineman Anthony Collins at right tackle. Collins was a fourth-round draft pick last year and started six games at right tackle because of injuries.

The line has undergone an overhaul in the offseason. The Bengals made changes at center and at 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 in the preseason, and tore a ligament and a tendon in his passing elbow during the regular season, forcing him to miss a dozen 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 on Tuesday for the first time since he got hurt.

‘‘He looked remarkably improved,’’ Lewis said. ‘‘He looked pretty good. He was moving better.’’