McClure underwent surgery on his right knee Monday.
"He has been ruled out for that game, and we hope to have a better idea in terms of his rehabilitation," Smith told reporters. "The procedure went well, and he is in very good spirits. If there is anybody who can get back quicker than the timeline, it's Todd McClure."
McClure's streak of 144 consecutive games started will end when he sits out in Week 1. A seventh-round draft pick of the Falcons in 1999, he has started 172 of 175 career games, including six in the playoffs. He was injured in Atlanta's preseason loss Saturday at Pittsburgh.
Joe Hawley, a fourth-round pick from UNLV last year, is working in McClure's spot and will start the preseason finale Thursday against Baltimore.
Information from The Associated Press was used in this report.