McCown left Thursday's 56-14 loss to the Falcons with a hand injury. Backup Mike Glennon, the team's third-round pick in 2013, completed 17 of 24 passes for 121 yards and a touchdown after replacing McCown.
Smith said there will no change to the team's lineup based on Thursday's game.
"Josh is our starter."
The Buccaneers are 0-3 and are last in the NFL in passing yards, averaging 163.3 yards per game.
Tampa Bay will play the Pittsburgh Steelers in Week 4.
- Paul Palladino