Coach Mike Smith said Motta suffered the injury during Thursday's practice.
"It flared up over the night,'' Smith said.
Motta already has been dealing with a broken finger on his right hand. He was forced to play with a cast due to that injury.
Fortunately for the Falcons, veteran safety Thomas DeCoud is cleared to play this week coming off a concussion. DeCoud missed last Sunday's game, which resulted in Motta's first start.
DeCoud had full participation Friday,
Linebacker Sean Weatherspoon (knee) and wide receiver Darius Johnson (high-ankle sprain) also were held out of Friday's practice, while running back/special-teamer Antone Smith (knee) returned to practice but was limited.
Tight end Tony Gonzalez (toe) was limited once again, but he's expected to play in Monday night's game at San Francisco.